how do i solve for this? (trigonometry)

The angle of elevation of the top of a cliff from the point on the ground is 30°. On a moving distance of 15m towards the foot of the cliff, the angle of elevation increases. If the height of the cliff is 17.3m, find the new angle of elevation to the nearest degree.

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misa4437 misa4437 · Answer 1 · 2024-03-09T22:54:57+01:00

Let the new angle of elevation of the rock after increasing the distance to 15 m be x degrees.

Since the initial angle of elevation of the cliff top from a point on the ground is 30°, we can make the following equation:

tan(30°) = height of the cliff / distance to the top of the cliff

Thus, the height of the rock will be equal to:

the height of the rock = 15 * tan(30°) = 15 * 0.5774 = 8.66 m

Now we will find the new height of the cliff after increasing the distance to the foot of the cliff to 15 m:

the new height of the cliff = 17.3 - 8.66 = 8.64 m

Now let's make a new equation:

tan(x) = new cliff height / 15

tan(x) = 8.64 / 15

x = arctan(8.64 / 15)

x ≈ 29.15°

So, the new angle of elevation of the rock after increasing the distance is 29°.