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Help ASAP. A carpenter builds a ramp from the level ground to a platform that is 2 ft high. If the length of the ramp is 8 ft 6 in. long, what is the angle measure the ramp makes with the ground, to the nearest degree? A. 7° B. 14° C. 17° or D. 30°

Respuesta :

calculista

Answer:

B. 14°

Step-by-step explanation:

Let

x ---> the length of the ramp

y ---> the high of the ramp

[tex]\theta[/tex] -----> the angle measure the ramp makes with the ground

we know that

[tex]sin(\theta)=\frac{y}{x}[/tex] ----> by SOH (opposite side divided by the hypotenuse)

Remember that

[tex]1\ ft=12\ in[/tex]

we have

[tex]y=2\ ft[/tex]

[tex]x=8\ ft\ 6\ in=8+(6/12)=8.5\ ft[/tex]

substitute

[tex]sin(\theta)=\frac{2}{8.5}[/tex]

using a calculator

[tex]m\angle \theta=sin^{-1}(\frac{2}{8.5})=14^o[/tex]

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