Problem

At a certain point on the ground, the tower at the top of a 50-m-high building subtends as angle of 25°. At another point on the ground 30 m closer the building, the tower subtends an angle of 25°. Find the height of the tower.

A. 65.3 m

B. 60.8 m

C. 75.1 m

D. 70.2 m

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Problem

An observer on the top of a cliff 150 m high above the angle of depression of two ships, which are due north him, to be 20° 12’ and 47° 39’. Find the distance between the ships in meters.

A. 290.76

B. 290.67

C. 270.69

D. 270.96

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Problem

From the top of a lighthouse 120 m above the sea, the angle of depression of a boat is 15°. How far is the boat from the lighthouse?

A. 463 m

B. 32 m

C. 124 m

D. 448 m

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Problem

A point inside an equilateral triangle is 3 cm, 4 cm, and 5 cm, respectively from each of its sides. What is the area of the triangle?

A. 89.54 cm²

B. 83.14 cm²

C. 96.25 cm²

D. 75.58 cm²

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Problem

Find the length of the altitude of an isosceles triangle if the base is 8 and the equal sides are 12.

A. 6√(3)

B. 6√(2)

C. 8√(2)

D. 8√(3)

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Problem (November 2019)

A 50-m supporting wire is to be attached to a 75-m antenna. Because of the surrounding building, sidewalks, and roadways, the wire must be anchored exactly 20 m from the base of the antenna. How high from the base of the antenna is the wire attached?

A. 44.8 m

B. 42.8 m

C. 45.8 m

D. 43.8 m

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Problem

Determine the integer values that the length of side a of the triangle can have if the other two sides have lengths 3 and 7.

A. 4, 5, 6

B. 4, 5, 6, 7, 8

C. 5, 6, 7, 8, 9

D. 4, 5, 6, 7, 8, 9

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Problem

The hypotenuse of a right triangle is 34in. Find the length of the two legs if one leg is 14in longer than the other.

A. 14 & 28

B. 16 & 30

C. 13 & 27

D. 16 & 29

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Problem

A river flows due south at 125 ft/min. A motorboat, moving at 475 ft/min in still water, is headed due east across the river. In what direction must the boat be headed in order to move due east, and what is its speed in that direction?

A. N75°20’E, 491 ft/min

B. N72°50’E, 419 ft/min

C. N74°40’E, 458 ft/min

D. N73°10’E, 485 ft/min

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Problem

The parallel sides of a trapezoidal lot measure 160 m and 240 m and are 40 m apart. Find the length of the dividing line parallel to the two sides that will divide the lot into two equal areas.

A. 185.92

B. 203.96

C. 195.55

D. 211.33

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Problem

A quadrilateral ABCD is inscribed in a circle with CD as diameter. AB is parallel to CD and AB is shorter than CD. If the measure of the angle ABD is 40°, determine the measure of angle ADB.

A. 10°

B. 12.5°

C. 15°

D. 20°

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