Question

What is the length of the altitude to longest side of a triangle, if the lengths of its sides are: 15cm, 17cm, 8cm? Thank you!

Answer 1

The length of the altitude to longest side of a triangle : 7.059 cm

Further explanation

Triangles are flat fields bounded by 3 intersecting sides and 3 angles

This side can be the same length or different.

Altitudes (h) are used to find the area of a triangle

$\rm A=\dfrac{1}{2}\times base\times altitudes (h)$

If we know the lengths of all three sides, we can use Heron's formula to find out the area of the triangle

the Area:

$\rm A=\sqrt{ (s (s-a) (s-b) (s-c))}$

where

s = semi-perimeter / half of the triangles perimeter

$\rm s=\dfrac{a+b+c}{2}$

a, b, and c are side lengths

The lengths of the sides of a triangle: 15cm, 17cm, 8cm

Longest side: 17 cm

Then :

$\rm s=\dfrac{a+b+c}{2}\\\\s=\dfrac{15+17+8}{2}\\\\s=20$

the Area:

$\rm A=\sqrt{(s (s-a) (s-b) (s-c))}\\\\A=\sqrt{20 (20-15) (20-17) (20-8)}\\\\A=60$

The length of the altitude to the longest side (17 cm) can be searched from:

$\rm A=\dfrac{1}{2}\times base\times h$

$\rm 60=\frac{1}{2}\times 17\times h\\\\60=8.5\times h\\\\h=60:8.5\\\\h=\boxed{\bold{ 7,059}}$

Learn more

the Sin rule

brainly.com/question/3324288

trigonometric ratios

brainly.com/question/10782297

the triangle angle

brainly.com/question/1611320

Answer 2

Answer:

The answer for this is 7.059

Step-by-step explanation: