ECAT Pre Engineering MCQ Test With Answer for Chapter 14 Mathematics

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  A
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  B
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  C
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  D

IfΔABC is right, law of cosine reduce to

• Law of sine A
• Law of tangent B
• Phthogorous theorem C
• Hero's formula D

120° degrees are equal to how many radians?

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  A
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  B
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  C
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  D

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  A
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  B
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  C
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  D

If the elevation of the sun is 30°, then the length of the shadow cast by a tower of 150 ft height is

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  A
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  B
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  C
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  D

PQ is a post of given height a, and AB is a tower at some distance;αandβare the angles of elevation of B, the top of the tower, at P and Q respectively. The height of the tower and its distance from the post are

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  A
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  B
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  C
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  D

A circle passing through the vertices of any triangle is called

• Circumcirle A
• Incircle B
• Escribed circle C
• Unit circle D

A tower subtends an angleαat a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower isβ. The height of the tower is

• b cotαtanβ A
• b tanαtanβ B
• b tanαcotβ C
• None of these D

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  A
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  B
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  C
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  D

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  A
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  B
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  C
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  D

Area ofΔABC=

• ab sinα A
• 1/2 ab sinα B
• 1/2 ac sinγ C
• 1/2 ac sinβ D

A triangle has six

• side A
• elements B
• angle C
• tangents D

The angle of elevation of the top of a tree from a point 17 meters from is foot is 42^𝜊The height of the tree is

• 12m A
• 21m B
• 17m C
• 15m D

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  A
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  B
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  C
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  D

• R A
• 2R B
• r C
• 2r D

If sided of𝜟ABC are 16,20,and 33, then the value of the greatests angle to

• 150𝜊 20' A
• 132𝜊 35' B
• 101𝜊 25' C
• 160𝜊 50' D

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is

• 40 m A
• 30 m B
• 20 m C
• 60 m D

A vertical pole is 8m high and the length of its shadow is 6m. The angle of elevation of the sun of the moment is

• 57𝜊 A
• -48𝜊 B
• 27𝜊 C
• 53𝜊 D

The upper 3/4 the portion of a vertical pole subtends an angle tan^-13/5 at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is

• 20 m A
• 40 m B
• 60 m C
• 80 m D

The longer side of a parallelogram is 10 cm and the shorter is 6 cm. If the longer diagonal makes an angles 30° with the longer side, the length of the longer diagonal is

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  A
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  B
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  C
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  D

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  A
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  B
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  C
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  D

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  A
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  B
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  C
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  D

The angle of elevation of a tower from a point A due south of it is x and from a point B due east of A is y. If AB = 1, then the height h of the tower is given by

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  A
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  B
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  C
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  D

Ifθ= 60° then

• sinθ= 1/2 A
• tanθ= cot 30° B
• θ=π/4 C
• secθ= 4 D

The angle of depression of a point situated at a distance of 70 meters from the base of a tower is 45°. The height of the tower is

• 70 m A
• 85 m B
• 35 m C
• None of these D

A tower subtends an angle of 30° at a point distant d from the foot of the tower and on the same level as the foot of the tower. At a second point, h vertically above the firs, the angle of depression of the foot of the tower, is 60°. The height of the tower is

• h/3 A
• h/3d B
• 3h C
• 3h / d D

The towers each 120 meters high are 800 meters apart. The measure of the angle of elevation from the base of one tower to the top of the other is

• 12^𝜊 A
• 9^𝜊 B
• 7^𝜊 C
• -120^𝜊 D

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  A
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  B
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  C
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  D

The law of sines can be used to solve oblique triangle when following information is given:

• Two angles and a side A
• Two sides and an angle opposite one of the given sides B
• Two sides and the angle between two sided C
• Option a and b D

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  A
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  B
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  C
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  D