Trees in a local park are hundreds of feet tall The height o

Trees in a local park are hundreds of feet tall. The height of one of these trees is represented by h in the figure shown. Use the measurements shown to find a, to the nearest tenth of a foot, in oblique triangle ABC. The length of a is approximately feet. (Do not round until the final answer. Then round to the nearest tenth as needed.) Use the right triangle shown to find the height, to the nearest tenth of a foot, of the tree in the park. The height of the tree, h, is approximately feet. (Do not round until the final answer. Then round to the nearest tenth as needed.)

Solution

from fig in triangle ABC, angle A = 15

from fig: angle B = 180 - 25 = 155

since A+B+C = 180 degree ( sum of all the angles)

so angle C = 180 - 15 - 155 = 10 degree

from sine formula , in triangle ABC:

sin 15 / a = sin 10 / 525

a = sin 15 * 525 / sin10 = 782.5 feet

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b) h = height = ?

from fig ,in right angle triangle : [ from sin ( theta) = perpendicular / hypotenuse]

sin 25 = h / a

h = sin 25* ( 782.5)

h = 330.69 feet