Question

Question is in image and the answer options I put are the answers I was given to choose from!

Answer 1

Given

The right triangles are given

In a part , the sides of the triangle is given 12 and 5.

In b part , all the sides are given 8,7,4.

Step-by-step explanation

a. To determine the hypotenuse side.

Use the Pythagoras theorem

`Hypotenuse^2=Perpendicular^2+base^2`

Substitute the values.

`\begin{gathered} c^2=12^2+5^2 \\ c^2=144+25 \\ c=√(169) \\ c=13 \end{gathered}`

b. To determine the ratios of trigonometric function from the right triangle.

Using the trigonometric ratios of sine , cosine and tan

`\begin{gathered} sinC=(4)/(8) \\ sinC=(1)/(2) \end{gathered}`

For cosine,

`cosC=(7)/(8)`

For tangent,

`tanC=(4)/(7)`Answer

Hence the answers are

a. The hypotenuse is c=13.

b. The trigonometric ratios are

`\begin{gathered} sinC=(1)/(2) \\ cosC=(7)/(8) \\ tanC=(4)/(7) \end{gathered}`