Question

ABC is a right triangle with C=90°. Solve for all missing parts given that A=25° and c=80m.

Answer 1

To solve the question we have to draw the triangle with the given information

Since the sum of the angles of any triangle is 180 degrees, then

Subtract
`\begin{gathered} m\angle B=180-25-90 \\ m\angle B=65^(\circ) \end{gathered}`We will use the trigonometry ratios to find a, b

`\begin{gathered} \sin A=(a)/(c) \\ \cos A=(b)/(c) \end{gathered}`

Since c = 80, then

`\sin (25)=(a)/(80)`

By using cross multiplication

`\begin{gathered} a=80\sin (25) \\ a=33.81m\rightarrow(2d.p) \end{gathered}`
`\begin{gathered} \cos (25)=(b)/(80) \\ b=80\cos (25) \\ b=72.50m\rightarrow(2d.p) \end{gathered}`

The missing in the triangles are:

m

a = 33.81 to the nearest 2 d.p

b = 72.50 to the nearest 2 d.p