Using the trigonometric ratios, the measures are:
a. z = 222.5 ft
b. h = 38.6 ft.
c. b = 10.4 ft
d. B = 219.1 ft.
What are the Trigonometric Ratios?
The ratios of trigonometry that can be used to solve a right triangle are:
sin ∅ = opp/hyp
cos ∅ = adj/hyp
tan ∅ = opp/adj.
a. Find h using the sin ∅ = opp/hyp:
sin 75 = opp/hyp = h/40
h = (sin 75)(40) = 38.6
Find z using the sin ∅ = opp/hyp
sin 10 = opp/hyp = 38.6/z
z = 38.6/sin 10
z = 222.5 ft. (length of the zip line)
b. Height of the tree = h = 38.6 ft.
c. Using sin ∅ = opp/hyp, find b (distance between the base of the ladder and the base of the tree):
sin 15 = b/40
b = (sin 15)(40)
b = 10.4 ft
d. Using sin ∅ = opp/hyp, find B as shown in the image:
sin 80 = opp/hyp = B/222.5
B = (sin 80)(222.5)
B = 219.1 ft.
Learn more about the trigonometric ratios on:
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