Question

 

Find the value of x. Round to the nearest tenth. Drawing not to scale. 

	A.	12.9
	B.	8.5
	C.	12.4
	D.	8.1

 

 

An engineer is surveying a building with a device that is 5 feet above the ground. He is 50 feet from the building and is looking with an angle of elevation of 50°. How tall is the building?

	A.	64.59 ft
	B.	59.59 ft
	C.	54.59 ft
	D.	69.59 ft

 

 

Find the value of x. Round the lengths to the nearest tenth. Drawing are not to scale. 

	A.	7.6 ft
	B.	10.6 ft
	C.	15.3 ft
	D.	7.9 ft

 

Answer 1

1) 

Recall the basic trigonometric ratios

cos(θ) = Adjacent side/Hypotenuse

cos(36^o) = x/10

0.809 = x/10

x =10*0.809

x = 8.09

x ≈ 8.1

Option D is correct.

Answer 2

2)

Draw the diagram:

Height of the building x = BD+ DF = 5 + +DF

Find the value of DF from the △ DEF.

Recall the basic trigonometric ratios

tan(θ) = Opposite side/Adjecent side

tan(50^o) = DF/50

1.192 = DF/50

DF =50*1.192

DF = 59.59

Height of the building x = 5 + +DF = 5 + 59.59 = 64.59

x =64.59

Option A is correct.

Answer 3

Recall the basic trigonometric ratios

cos(θ) = Adjacent side/Hypotenuse

cos(44^o) = x/11

0.719 = x/11

x =11*0.719

x = 7.913

x ≈7.9

Option D is correct.