A 24-foot ladder leaning against a wall makes a 30 ° angle with the ground . How high up on the building is the top of the ladder ? HE

Question

A 24-foot ladder leaning against a wall makes a 30 ° angle with the ground . How high up on the building is the top of the ladder ?
HELP ASAP

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Thạch Thảo 3 years 2021-08-24T21:43:59+00:00 1 Answers 5 views 0

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  1. kiet
    0
    2021-08-24T21:45:03+00:00
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    Answer:

    12\:\mathrm{ft}

    Step-by-step explanation:

    When the ladder is leaning against the wall, a 30-60-90 triangle is formed. The ladder acts as a 24-foot hypotenuse. Because the height is facing the 30^{\circ} angle, the height is half the hypotenuse (30-60-90 rules). If you forget the side rules for a 30-60-90 triangle, simply use basic trig on the right triangle:

    \sin 30^{\circ}=\frac{h}{24},\\h=24\sin 30^{\circ},\\h=24\cdot \frac{1}{2},\\h=\fbox{$12\:\mathrm{ft}$}.

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