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