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Max is installing a 12-ft swimming pool slide at a 50° angle of elevation. The bottom of the slide will be 1 foot off the ground and the top of the slide will be fixed to a platform. Find the height of the platform. (round to nearest tenth)

Respuesta :

Answer:

10.2 ft

Step-by-step explanation:

The swimming pool would make a right triangle with the pool, if the bottom of the slide touched the bottom of the pool.  

If we take the right triangle that would be formed, we have the 50° angle of elevation and the hypotenuse of the triangle, 12.

We are trying to find the height of the platform; this would be the side opposite the 50° angle.  The ratio of opposite/hypotenuse is sine; this gives us the equation

sin 50 = x/12

Multiply both sides by 12:

12sin 50 = (x/12)(12)

12sin 50 = x

9.2 = x

Since the bottom of the slide is 1 foot above the ground, the height of the platform is 9.2+1 = 10.2.

good job