Question

find the area of triangle qpm. round the answer to the nearest tenth. a. 5.2 square units b. 6.3 square units c. 6.5 square units d. 12.6 square units

Answer 1

Pls. see attachment. 

We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.

Given:

51 degrees.

Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.

180 – 51 – 90 = 39 degrees

39 degrees * 2 = 78 degrees.

Angle Q is 78 degrees.

In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.

We will use the formula:

Sine theta = opposite / hypotenuse

Sin(78 deg) = opposite / 4.3

Sin(78 deg) * 4.3 = opposite

4.21 = opposite. This is also the height of the triangle.

 

Area of a triangle = ½ * base * height

A = ½ * 3units * 4.21units

A = 6.315 square units.