Question

For the right triangle, find the missing quantity indicated below the figure round to nearest tenth

Answer 1

We are given a right-angled triangle.

The given angle is 50°40'

Let us convert the minute part to degrees

`\begin{gathered} (40^(\prime))/(60)=0.67\degree \\ 50\degree+0.67\degree=50.67\degree \end{gathered}`

With respect to the angle 50.67°, the adjacent side is 17.2' and the opposite side is b.

Recall from the trignonometric ratios,

`\tan \theta=(opposite)/(adjacent)`

For the given case, we have

θ = 50.67°

Adjacent = 17.2'

Opposite side = b

Let us substitute these values into the above formula to find the value of b.

`\begin{gathered} \tan (50.67\degree)=(b)/(17.2) \\ b=\tan (50.67\degree)\cdot17.2 \\ b=1.2205\cdot17.2 \\ b=21.0^(\prime) \end{gathered}`

Therefore, the value of b is 21.0'