Solve the problem. Be sure to make a diagram of the situation with all the given information labeled. The two equal sides of an isosceles triangle are each 44 centimeters. If the base measures 30 centimeters, find the height and the measure of the two equal angles. Round your answers to the whole numbers.

A)The height is 42 cm; the angles are 70°.
B)The height is 44 cm; the angles are 72 ° .
C)The height is 41 cm; the angles are 70 ° .
D)The height is 39 cm; the angles are 70 ° .
E)The height is 41 cm; the angles are 72 ° .

Question

Solve the problem. Be sure to make a diagram of the situation with all the given information labeled. The two equal sides of an isosceles triangle are each 44 centimeters. If the base measures 30 centimeters, find the height and the measure of the two equal angles. Round your answers to the whole numbers.
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A)The height is 42 cm; the angles are 70°.
B)The height is 44 cm; the angles are 72 ° .
C)The height is 41 cm; the angles are 70 ° .
D)The height is 39 cm; the angles are 70 ° .
E)The height is 41 cm; the angles are 72 ° .

Quizplus · Accepted Answer

We can use the formula for the area of a triangle: 
Area = 0.5 x base x height.

Substituting the given values, we have:

Area = 0.5 x 30 cm x height

Since the triangle is isosceles, we can draw an altitude from the apex (top vertex) to the base, splitting it into two equal segments. Let's call the height h and label it on the diagram.

By the Pythagorean theorem, we have:

(44 cm)^2 = (0.5 x 30 cm)^2 + h^2

Simplifying this equation, we get:

h = sqrt(44^2 - 15^2) = 41 cm

Therefore, the height is 41 cm.

To find the angles, we can use the fact that the sum of the angles in a triangle is 180 degrees. Let's label the two equal angles as x, as shown in the diagram.

We have:

x + x + 180 - 2x = 180

Simplifying this equation, we get:

x = 70 degrees

Therefore, the two equal angles are 70 degrees.

The answer is choice C: The height is 41 cm; the angles are 70 degrees.

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