Question

In ∆OPQ the measure of

Answer 1

To answer this question, we can use one of the trigonometric ratios since we have a right triangle here. We also need to know that the reference angle is Having this information into account, we can use the following trigonometric ratio:

`\tan (\theta)=(opp)/(adj)`

That is, we have the value of the opposite side, and we will have the value for tan(5). Then, we have:

`\tan (5)=(QP)/(QO)=(4.6)/(QO)`

Now, we have to solve the equation for QO:

1. Multiply each side of the equation by QO:

`QO\cdot\tan (5)=(4.6)/(QO)\cdot QO\Rightarrow QO\cdot\tan (5)=4.6`

2. Divide both sides of the equation by tan(5):

`QO\cdot(\tan(5))/(\tan(5))=(4.6)/(\tan(5))\Rightarrow QO=(4.6)/(\tan (5))`

Therefore, we have that QO is:

`QO=(4.6ft)/(0.0874886635259)\Rightarrow QO=52.5782405927ft`

If we rounded this value to the nearest tenth, we have that QO = 52.6 ft.