Triangle ABC is given where m(angle)A=33 degrees, a=15 in., and the height, h, is 9 in. How many distinct triangles can be made with the given measurements? Explain your answer.

One triangle

Step-by-step explanation:

Find the measures of the triangle ABC

Let

D ----> intersection point of the height triangle ABC with the segment AB

step 1

Find the measure of angle B

In the right triangle BCD

---> by SOH (opposite side divided by the hypotenuse)

substitute the given values

using a calculator

step 2

Find the length of segment DB in the right triangle BCD

Applying the Pythagorean Theorem

substitute

step 3

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

substitute the given values

step 4

Find the length side AC

In the right triangle ACD

---> by SOH (opposite side divided by the hypotenuse)

substitute the given values

solve for AC

step 5

Find the length of segment AD

In the right triangle ACD

---> by TOA (opposite side divided by the adjacent side)

substitute the given values

step 6

Find the length side AB

substitute the given values

step 7

The measures of triangle ABC are

so

The measurements of the ABC triangle are unique

therefore

Only one triangle can be constructed  with the given measurements

x=half

step-by-step explanation: