Re-write 15/9 as a mixed number
1 answer:
You might be interested in
<h3>Answer:</h3>
The altitude to T is 9.6 cm
The altitude to S is 8 cm
The altitude to P is 9.6 cm
<h3>Explanation:</h3>∆TSP is isosceles, so the altitude to TP from S will bisect TP (at point A) and create two right triangles, each with a base of (12 cm)/2 = 6 cm and a hypotenuse of 10 cm. The Pythagorean theorem tells you ...
... SP² = SA² +AP²
... (10 cm)² = SA² + (6 cm)²
... (100 -36) cm² = SA² = 64 cm²
... SA = √(64 cm²) = 8 cm . . . . the altitude to S
_____
The altitude to the other sides can now be found from the area of the triangle. The area of ∆TSP is ...
... A = (1/2)bh = (1/2)·TP·SA
... A = (1/2)(12 cm)(8 cm) = 48 cm²
We can call the point on SP where the altitude from T intersects it point B. Then the area is the same using base SP and altitude TB.
... A = (1/2)bh = (1/2)·SP·TB
... 48 cm² = (1/2)(10 cm)·TB
... (48 cm²)/(5 cm) = TB = 9.6 cm . . . . the altitude to T
The altitude from P to TS, the other side of length 10 cm, will be the same. The altitude to P is 9.6 cm.