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silvermansachs9189
15.10.2019 •
Mathematics
Tony is standing at sea level. from his location, the angle of elevation of the top of blue mountain is 25°. staying at sea level, he walks 200 yards toward the mountain. the angle of elevation of the top is now 30°. find the height of blue mountain. round intermediate results to 3 decimal places and the final answer to 1 decimal place.
the height of blue mountain is yards
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Ответ:
h = 1558.8
Step-by-step explanation:
Let x be the distance from the vertex of the 30 degree angle to the base of Blue mountain.
Tan (30) = h/x Multiply both sides by x.
x * Tan(30) = h
Tan(25) = h/(x + 200) Multiply x + 200 on both sides.
(x + 200) * Tan(25) = h
Now you have 2 equations both equal to h. The two sides can be equated to each other.
x*tan(30) = (x + h) * Tan(25) Divide both sides by tan(25)
x*tan(30)/tan(25) = x + 200 Find Tan(30)/Tan(25)
Tan30 / tan(25) = 1.23813 so
1.23813 x = x + 200 Subtract x from both sides.
0.23813x = 200 Divide both sides by 0.23813
x = 200/0.23813
x = 839.99
That is not the answer you have been asked for. What you need is h.
Tan(30) = x / h Multiply both sides by h
h*tan(30) = x Divide both sides by tan(30)
h = x/tan(30)
h = 839.99/tan(30) Tan 30 = 0.57735
h = 839.99/0.57735
h = 1558.8
Ответ: