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 t
he 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.
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
