Question

Igor’s pet bat Natasha is flying at the end of a 50 ft leash anchored to the

ground, Using a clinometer, he spots Natasha at a 55° angle from the base of
the bat’s leash. How high is Natasha?
6. Meteorologist Wendy Storm is using a clinometer and a ceiling light to
measure the base of a cloud. When she is standing 1000 ft from the ceiling
light, she measure the angle to the spot on the cloud at 77°. Rounded to the
nearest 100 ft, how high is the cloud,?
7. The angle of elevation from a ship to the top of a 42 m lighthouse, on the
shore, is 33°. How far is the ship from the shore?
8. Ben is flying a kite with 125 m of string out. His kite string makes a 39°
angle with the ground. How high is his kite?
9. Chip Woodman, the foreperson of a paper plant, must make an estimate of the
height of the cone shaped wood pile. The distance from the tip of the cone, to
the base (slant height), is 304 ft and forms a 54° angle. How high is the cone
of wood.
10. Captain Bly Bligh observes a lighthouse 42° from the path of her ship. The
next sighting of the same lighthouse is at 90°. She has traveled 1.8 km between
sightings. How far is her ship away from the lighthouse at the second
sighting?
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Answer 1

Let's solve each problem step by step:

6. To find Natasha's height, use the tangent of the angle: \( \tan(55°) = \frac{\text{height}}{50 \text{ ft}} \). Solve for the height.

7. For the cloud's height, again use the tangent: \( \tan(77°) = \frac{\text{height}}{1000 \text{ ft}} \). Solve for the height.

8. The kite's height is given by \( \tan(39°) = \frac{\text{height}}{125 \text{ m}} \). Solve for the height.

9. Using the tangent, \( \tan(54°) = \frac{\text{height}}{304 \text{ ft}} \), solve for the height of the cone.

10. For Captain Bly Bligh's ship distance, use the tangent between the two sightings: \( \tan(90° - 42°) = \frac{\text{distance traveled}}{\text{distance from lighthouse}} \). Solve for the distance from the lighthouse at the second sighting.

Please note that you can use a scientific calculator or trigonometric tables to find the tangent values and then solve for the unknowns. If you have specific values, I can assist with the calculations.