Question

Right triangle trigonometry word problems help

Answer 1

60.16 degrees


........

Answer 2

`60.16 \text{ meters}`

Explanation:

First, we must review our trig functions:

`\sin(\theta)=(opposite)/(hypotenuse) \\\cos(\theta)=(adjacent)/(hypotenuse) \\\tan(\theta)=(opposite)/(adjacent)`

For this problem, we are given a 76° angle and an adjacent side 15 meters long. We also know from our diagram that the width of the river is the length of our opposite side.

From this, we know the following:
`\tan(75^(\circ))=(opposite)/(15)`

Therefore:
`15 * \tan(75^(\circ))=opposite`

`opposite = 60.16 \text{ meters}`