Question

For triangle ABC, ∡c=90°, b=5, and ∡A=72°. Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.

Answer 1

The angle A is given 72 degree and angle C is given 90 degree.

The side b is 5.

Then the right triangle is given

Use the property , the sum of the angles of the property is the 180 degree.

`90^(\circ)+72^(\circ)+\angle B=180^(\circ)`
`\angle B=180^(\circ)-90^(\circ)-72^(\circ)`
`\angle B=18^(\circ)`

Then the angle B is 18 degree.

Then to determine side a , use the tan trigonometric function.

`\tan 72^(\circ)=(a)/(5)`
`a=5* tan72^(\circ)=15.38`

The side a is 15.38.

Now to determine the side c, use the trigonometric function sin .

`\sin 72^(\circ)=(a)/(c)=(15.38)/(c)`
`c=(15.38)/(\sin 72^(\circ))=16.18`

The side c is 16.18.