Precalculus

1. A man stands 12 feet from a statue. The angle of elevation from the eye level to the top of the statue is 30 degrees, and the angle of depression to the base of the statue is 15. How tall in the statue?

2. Two boats lie on a straight line with the base of a lighthouse. From the top of the lighthouse, 21 meters above water level, it is observed that the angle of depression of the nearest boat is 53 degrees and the angle of depression of the farthers boat is 27 degrees. How far aprt are the boats?

1. 👍
2. 👎
3. 👁
1. #1 My diagram has two right angle triangles with a common right angle, the one with the 53 angle embedded within the larger one.

label the distance from the nearer boat to the lighthouse x, label the distance from the farther boat to the lighthouse y

then tan53 = 21/x
x = 21/tan53

and tan 27 = y/21

distance between the two boats = y-x

#1 (similar to #2)

my diagram has the man standing 12 to the left of the statue, A the top, B the bottom, the line to the top makes an angle of 30º and to the bottom of the statue 15º
draw a horizontalline from the "eye" to the statue meeting it at P
use the tangent ratio twice to find AP and BP
height of statue = AP + BP

1. 👍
2. 👎
2. i still am confused on what to do for the second explanation you gave

1. 👍
2. 👎
3. ok,
draw a triangle ABE with AB a vertical line, that is your statue.
E is to left of the line AB
Join EA and EB
From E draw a line perpendicular to AB to meet AB at P, P is between A and B
EP = 12

angle AEP=30º
angle BEP = 15º

in top triangle:
AP/12 = tan 30
AP = 12tan30 = 6.928

in bottom triangle
BP/12 = tan15
BP = 12tan15 = 3.215
AB = 10.14

1. 👍
2. 👎

Similar Questions

1. trig

A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 24. From a point 1000 feet closer to the

2. Algebra2

A surveyor stands 150ft from the base of a tree and measures the angle of elevation to be 46.2. His eye level is 6feet above the ground. What is the height of the tree to the nearest foot?

3. Trigonometry

a flagpole 25 feet tall stands on a top of a building. from a point in the same horizontal plane with the base of the building. The angle of elevation of the top and the bottom are 61°30' and 56°20' respectively. How high is the

4. trig

A tunnel for a new highway is to be cut through a mountain that is 260 feet high. At a distance of 200 feet from the base of the mountain, the angle of elevation is 36 degrees. From a distance of 150 feet on the other side of the

1. alge

The angle of elevation of the sun is 31 degrees. Find the length of the shadow, to the nearest foot, of a man that is 6 feet tall.

2. Math

A, B and C are 3 points on the level ground.B is due south of A . The baering of C from A is 085. A vertical mast of height 50m stands at A. The angle of elevation of T from B is 44 and the angle of elevation of T from C is 28

3. GEOMETRY

A PERSON STANDING 30 FEET FROM A FLAGPOLE CAN SEE THE TOP OF THE POLE AT A 35 DEGREE ANGLE OF ELEVATION. THE PERSON'S EYE LEVEL IS 5 FEET FROM THE GROUND. FIND THE HEIGHT OF THE FLAGPOLE TO THE NEAREST FOOT.

4. math

A 1.7-metre tall man stands 12 m from the base of a tree. He views the top of the tree at an angle of elevation of 58°. How tall is the tree?

1. trig

A plane is flying 12,000 feet horizontally from a tall, vertical cliff. The angle of elevation from the plane to the top of the cliff is 45degrees, while the angle of depression from the plane to a point on the cliff at elevation

2. Math

A scuba diver dove from the surface of the ocean to an elevation of −59 9/10 feet at a rate of −15 feet per minute. After spending 12 minutes at that elevation, the diver ascended to an elevation of −38 9/10 feet. The total

3. math

An observer stands 25 feet from the base of a 50 foot flagpole and watches a flag being lowered at a rate of 5 ft/sec. Determine the rare at which the angle of elevation from the observer to the flag is changing at the instant

4. MATH - HELP ME PLEASE!!!!

The front of an A-frame cottage has the shape of an isosceles triangle. It stands 30 feet high and is 20 feet wide at its base. What is the angle of elevation of its roof? (Round your answer to two decimal places.)