Two residential buildings are to be constructed with a grassy recreational area between them. The taller building is 700 ft high. From the roof of the shorter building, the angle of elevation to the top of the taller building is 78 ° and the angle of depression to the base of the taller building is 62 ° . a. How tall is the shorter building? Round to the nearest foot b. What is the distance between the buildings? Round to the nearest foot
Two residential buildings are to be constructed with a grassy recreational area between them. The taller building is 700 ft high. From the roof of the shorter building, the angle of elevation to the top of the taller building is 78 ° and the angle of depression to the base of the taller building is 62 ° . a. How tall is the shorter building? Round to the nearest foot b. What is the distance between the buildings? Round to the nearest foot
Solution Summary: The author explains the angle of elevation from the shorter building to the top of the higher building is 78°. Then, draw a rough sketch for the considered conditions and label the sides and angles.
Two residential buildings are to be constructed with a grassy recreational area between them. The taller building is
700
ft
high. From the roof of the shorter building, the angle of elevation to the top of the taller building is
78
°
and the angle of depression to the base of the taller building is
62
°
.
a. How tall is the shorter building? Round to the nearest foot
b. What is the distance between the buildings? Round to the nearest foot
4
In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and
evaluate the integral. Hint: Find the limits on r and s by sketching the area of integration in the (x, y) plane along
with the r and s axes, and then show that the same area can be covered by s from 0 to r and r from 0 to 1.
7. What are all values of 0, for 0≤0<2л, where 2 sin² 0=-sin?
-
5π
6
π
(A) 0, л,
and
6
7π
(B) 0,л,
11π
, and
6
6
π 3π π
(C)
5π
2 2 3
, and
π 3π 2π
(D)
2' 2'3
, and
3
4元
3
1
די
}
I
-2m
3
1
-3
บ
1
#
1
I
3#
3m
8. The graph of g is shown above. Which of the following is an expression for g(x)?
(A) 1+ tan(x)
(B) 1-tan (x)
(C) 1-tan (2x)
(D) 1-tan
+
X
-
9. The function j is given by j(x)=2(sin x)(cos x)-cos x. Solve j(x) = 0 for values of x in the interval
Quiz A: Topic 3.10
Trigonometric Equations and Inequalities
Created by Bryan Passwater
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