Trigonometry Answers

His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground. 

At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.

 ____________ feet 

Marco would like to hang a banner over his shoe store. He has two ladders and would like to know high above the ground each ladder will allow him to place the banner.

His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground. 

At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.

 ____________ feet 

A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at _______ feet.

Explain how you determined your answer (explain all work used to determine the answer).

Find the angle that the 15-foot ladder makes with the building. Round your answer to the nearest tenth. ____________ degrees

The 15-foot ladder makes a ________ degree angle with the building.

Explain and show the work you used to solve the problem. Justify the answer you have.

Will the 13-foot ladder make the same angle with the building? Justify your reasoning.

If Cot θ= 12/5 , and

Cos θ= 1/tan θ. Evaluate;

Cos2θ/sin θ + Cos θ

Solve the following triangles:

13. A side and a diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side, is 124°. Find the length of the other diagonal and the length of the other side.

14. A lighthouse is 10 miles northeast of a dock. A ship leaves the dock at noon, and sails east at a speed of 12 miles an hour. At what time will it be 8 miles from the lighthouse?

15.A vertical pole 35 feet high, standing on sloping ground, is braced by a wire which extends from the top of the pole to a point on the ground 25 feet from the foot of the pole. If the pole. subtends an angle of 30° at the point where the wire reaches the ground, how long is the wire?

16.A tower 125 feet high stands on the side of a hill. At a point 240 feet from the foot of the tower, measured straight down the hill, the tower subtends an angle of 25°. What angle does the side of the hill make with the horizontal?

1. Define/describe an isosceles spherical triangle. State its properties and use illustrations if necessary.

2.  An isosceles spherical triangle has an angle A=B= 54° and side b = 82°. Find the measure of the third angle.

3. Determine the value of angle B of an isosceles spherical triangle ABC whose given parts are b=c= 54°28’ and a = 92°30’

4. Solve for the side b of a right spherical triangle ABC whose parts of an isosceles spherical triangle are a = 46°, b = 75° and C = 90°.

A vertical aerial AB 12.65m high stands on ground which is inclined 18°32 15to the horizontal. A stay connects the top of the aerial A to a point Con the ground 20.0 m uphill from Bthe foot of the aerial.

Determine:

the length of the stay .

the angle the stay makes with the ground

Michael has a ladder set up to clean the gutters of his house. The top of the ladder reaches the base of the gutter, 30 feet from the ground. If the ladder is 32 feet tall, how far from the base of the house is the base of the ladder?

3. Given a frustum of a right circular cone with a slant height of 9ft ., and the radii of bases are 5ft and 7ft. Find:

a. The lateral area

b. Altitude of the frustum

c. The altitude of the entire cone if the cone removed was replaced

(e) Simplify a trigonometric expression sin θ cos² θ − sin θ

A= 82°, b=100°, c=78° Find: B