Question

1. At a horizontal distance of 34 meters from the base of a tower, the angle of elevation to the top is 72 degrees. Find the height of the tower to the nearest tenth of a meter.

2. From the top of a lighthouse 18 m high, the angle of depression to sight a boat is 4 degrees. To the nearest meter, what is the distance between the boat and the base of the lighthouse?

3. The foot of a 15 ft ladder is 8 foot from the side of a house. To the nearest tenth of a degree what angle does the ladder make with the ground?

4. A ladder is leaning against the side of a building and forms an angle of 68o with the ground. The foot of the ladder is 12 feet from the base of the building. Find the length of the ladder to the nearest foot.

5. An advertising blimp hovers over a stadium at an altitude of 125 m. The pilot sights a tennis court at an 8o angle of depression. To the nearest meter, find the ground distance in a straight line between the stadium and the tennis court.

6. A boat drops an anchor to the bottom of a lake. The anchor rope makes a 17 degree angle with the boat. The anchor rope is 24 feet long. To the nearest foot how deep is the lake?

7. A 12 ft. ladder makes a 33o angle with the side of a house. To the nearest tenth of a foot how high up on the house does the ladder come?

Answer 1

Part 1) At a horizontal distance of 34 meters from the base of a tower, the angle of elevation to the top is 72 degrees. Find the height of the tower to the nearest tenth of a meter.

we know that
tan 72=opposite side angle 72/adjacent side angle 72
opposite side angle 72-------> vertical distance (height of the tower h)
adjacent side angle 72°-------> horizontal distance-----> 34 m
so
tan 72=h/34------> h=34*tan 72-----> h=104.64 m-----> h=104.6 m

see the attached figure

the answer Part 1) is
h=104.6 m

Part 2) From the top of a lighthouse 18 m high, the angle of depression to sight a boat is 4 degrees. To the nearest meter, what is the distance between the boat and the base of the lighthouse?

see the picture attached to better understand the problem

we know that
tan 4=opposite side angle 4/adjacent side angle 4
opposite side angle 4-------> vertical distance---->18 m
adjacent side angle 4-------> horizontal distance---> dh
so
tan 4=18/dh-----> dh=18/tan 4-----> dh=257.41 m-----> dh=257 m

the answer Part 2) is
the distance between the boat and the base of the lighthouse is 257 m

Part 3)The foot of a 15 ft ladder is 8 foot from the side of a house. To the nearest tenth of a degree what angle does the ladder make with the ground?

see the picture attached to better understand the problem

cos ∅=AC/AB-------> tan ∅=8/15
∅=arc cos (8/15)-----> ∅=57.77°-----> ∅=57.8°

the answer part 3) is
∅=57.8°

Part 4) A ladder is leaning against the side of a building and forms an angle of 68° with the ground. The foot of the ladder is 12 feet from the base of the building. Find the length of the ladder to the nearest foot

see the picture attached to better understand the problem
we know that
cos 68=AC/AB------AB=AC/cos 68----> AB=12/cos 68
AB=32.03 ft----> AB=32 ft

the answer Part 4) is
the length of the ladder is 32 ft

Part 5)An advertising blimp hovers over a stadium at an altitude of 125 m. The pilot sights a tennis court at an 8° angle of depression. To the nearest meter, find the ground distance in a straight line between the stadium and the tennis court.
see the picture attached to better understand the problem

we know that
tan 8=AB/BC---------> BC=AB/tan 8-----> BC=125/tan 8----> BC=889.42 m

the answer part 5) is
the ground distance in a straight line between the stadium and the tennis court is 889 meters

Part 6) A boat drops an anchor to the bottom of a lake. The anchor rope makes a 17 degree angle with the boat. The anchor rope is 24 feet long. To the nearest foot how deep is the lake?

see the picture attached to better understand the problem

we know that
sin 17=AB/AC-----> AB=AC*sin 17----> AB=24*sin 17----> AB=7.02 ft

the answer Part 6) is
the deep of the lake is 7 ft

Part 7)A 12 ft. ladder makes a 33° angle with the side of a house. To the nearest tenth of a foot how high up on the house does the ladder come?
see the picture attached to better understand the problem

we know that
cos 33°=AB/AC-----> AB=AC*cos 33-----> AB=12*cos 33----> AB= 10.06 ft

the answer part 7) is
10.1 ft