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

need points to ask question

step-by-step explanation:

both equations and proportions are better.