A ladder on a fire truck can be extended to a maximum length of 21 m when elevated to its maximum angle of 70°. The base of the ladder is mounted on the truck 2.15 m above the ground. How high above the ground will the ladder reach? Round to the nearest tenth.

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A ladder on a fire truck can be extended to a maximum length of 21 m when elevated to its maximum angle of 70°. The base of the ladder is mounted on the truck 2.15 m above the ground. How high above the ground will the ladder reach? Round to the nearest tenth.

Mathematics
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To find the vertical distance the ladder stretches, draw a right triangle. The hypotenuse will be 21 meters and the angle between the hypotenuse and the truck will be 70 degrees. You have to find the opposite side of the triangle, so use sine (SOH). sin(70) = b / 21 --> b = 21sin(70) = 19.734 m. Add this to the 2.15 mount to get 21.889 meters for an answer.
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