Question

4.6 yd-12 ydO 348.8 yd²532.1 yd²O 385.6 yd2O 520.9 yd²6 yd10 yd5 yd

Answer 1

Step-by-step explanation

From the statement, we have a right triangle with:

• angle θ,

,

• opposite side OS = 7,

,

• hypotenuse H = 12,

and we must find the value of angle θ.

We also have Tom's resolution of the problem.

(1) From the resolution, we see that Tom computes the angle θ using the following formula:

`\cos\theta=(7)/(12).`

Adding the data above the sides, we have:

`\cos\theta=(7)/(12)=(OS)/(H)\Rightarrow\cos\theta=(OS)/(H)\text{ }✖`

From trigonometry, we know that this equation is wrong. The correct trigonometric relation is:

`\sin\theta=(OS)/(H).`

(2) Replacing the values OS = 7 and H = 12 in the correct trigonometric relation, we have:

`\sin\theta=(7)/(12).`

Solving for θ, we get:

`θ=\sin^(-1)((7)/(12))\cong35.7\degree.`Answer

• The mistake in Tom's resolution is that he used the incorrect trigonometric relation for the angle, the opposite side and the hypotenuse.

,

• Using the correct trigonometric relation, which involves a sine function instead of the cosine, we get θ ≅ 35.7°.