Question

Can someone help me please

Answer 1

Given:

The figure of a right angle triangle with legs a and 7, and hypotenuse c.

The measure of angle opposite to leg 7 is 30^\circ.

To find:

All the missing measures for the triangle.

Solution:

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees. So,

`30^\circ+90^\circ+\text{Missing angle}=180^\circ`

`120^\circ+\text{Missing angle}=180^\circ`

`\text{Missing angle}=180^\circ-120^\circ`

`\text{Missing angle}=60^\circ`

In a right angle triangle ,

`\sin\theta=(Perpendicular)/(Hypotenuse)`

`\sin (30^\circ)=(7)/(c)`

`(1)/(2)=(7)/(c)`

`c=7* 2`

`c=14`

In a right angle triangle,

`\tan \theta =(Perpendicular)/(Base)`

`\tan (30^\circ)=(7)/(a)`

`(1)/(√(3))=(7)/(a)`

`a=7* √(3)`

`a=7√(3)`

Therefore, the measure of the missing angle is 60 degrees. Side "a" has a length of 14 units and side "c" has a length of
`7√(3)` units.