Question

A bridge connects to a tunnel as shown in the figure. The bridge is 180 feet above the ground, At a distance of 235 feet atong the bridge out of the tunnel, the angle to the base and summit of the cliff is a right angle.
a. What is the height of the cuff? Round to the nearest whole number

b. How high is the cliff from base to summit? Round to the nearest whole number.

c. What is the value of d? Round to the nearest whole number.​

Answer 1

180^2 + 235^2 = (cliff base to point on bridge)^2
32400 + 55225 = 87625
so cliff base to point on bridge = sqrt of 87625.
Then notice 87625 + d^2 = (x+180)^2
since x^2 +235^2 = d^2,
substitute (x^2 + 235^2) for d^2, like this:
87625 + x^2 + 235^2 = (x+180)^2
87625 + x^2 + 55225 = x^2 + 360x + 32400
87625 + 55225 - 32400 = x^2 - x^2 +360x
360x = 110450
x = about 306.8 feet
h = x+180, so h = 486.8 feet
Remember d^2 = x^2 + 235^2, so
d^2 = 306.8^2 + 235^2
d^2 = 149354.6489
d = about 386.46 feet