there are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle.

Balloon 21 feet in air held by two ropes forming two right triangles. Rope 1 forms a base angle of 45 degrees. Rope 2 forms a base angle of 30 degrees.

If the hot air balloon is 21 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot? Type the numeric answer only in the box below.

Question

there are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle.

Balloon 21 feet in air held by two ropes forming two right triangles. Rope 1 forms a base angle of 45 degrees. Rope 2 forms a base angle of 30 degrees.

If the hot air balloon is 21 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot? Type the numeric answer only in the box below.

kropot72 · Answer

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$$\tan 30\ degrees=\frac{21}{d}$$
$$d=\frac{21}{\tan 30}$$