# Math

How do I figure out the height of a triangle?

The height of a triangle is defined as the perpendicular distance from an angle to a side. Now, since this is a right triangle, and depending on how it is situated, the height could be 10" or 12" if you observe from the two acute angles. But from the right angle, the height goes from the angle to AC (your hypotenuse). Finding this one will be tricky but can be done using the Pythagorean Theorem.

If you drop a height from the right angle to the hypotenuse, it breaks it into two parts. The length of one part is x (since we don't know and since the height doesn't perfectly bisect the hypotenuse), and the length of the other part is 15.62-x (since the total length is 15.62"). It really doesn't matter which side is x, but for my explanation, I'll use x as the side closer to the leg that is 10". This height creates two new right triangles, and you can use the Pythagorean Theorem to find out both the height and the missing side x.

One formula will end up being 10^2 = h^2 + x^2, and the other formula will end up being 12^2 = h^2 + (15.62-x)^2. You can solve the first equation to find that h^2 = 100 - x^2 and substitute that in to the second equation:

12^2 = h^2 + (15.62-x)^2
144 = 100 - x^2 + 243.9844 - 31.24x + x^2
144 = 343.9844 - 31.24x
-199.9844 = -31.24x
x = 6.4 (rounded)

Knowing this, we can find that missing height:
h^2 = 100 - x^2
h^2 = 100 - (6.4)^2
h^2 = 100 - 40.98
h^2 = 59.02
h = 7.68"

So it all depends on the specific height you're looking for - it's either 10", 12", or 7.68".

As for your trough, surface area is the sum of all the areas. Break your trough into parts that you can find areas of. If you're just looking for the outer surface area, for example, you have two triangles for the ends and two rectangles for the sides (assuming that it's an open trough). The area of the triangles is A = 0.5bh, and the area of the rectangle sides is A = bh (b in this case will be a side of the trianlge, 2, and h will be the length of the trough, 16). So just add up all the surfaces that will comprise your trough and you should have your surface area. (I'm not sure if you need to include the inside as well, but if so you need 2 triangles and 2 rectangles for the outside, and 2 triangles and 2 rectangles for the inside as well.)

Hey thanks... I forgot about the Pythagorean theory... LOL and I'm trying to figure out the missing side thinking its impossible, and as soon as I read Pythagorean theory on your answer I knew.

Thanks a lot T.

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### Algebra

Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 12 and its height is 8?

2. ### Math

1. Find the length of the missing side of the right triangle (A triangle is shown to have a base of 15 cm and a height of 8 cm. The slope of it is unmarked A. 289 cm B. 17 cm *** C. 23 cm D. 4.79 cm 2. Find the length of the

3. ### Trig

An isosceles triangle has a height of 12.5 m (measured from the unequal side) and two equal angles that measure 55°. Determine the area of the triangle. Split in half the triangle is a right triangle, so it's three angles are

4. ### Calculus

The base of a triangle is shrinking at a rate of 1 cm/min and the height of the triangle is increasing at a rate of 6 cm/min. Find the rate (in cm2/min) at which the area of the triangle changes when the height is 38 cm and the

1. ### math --- pls check my work!

help pls asap!!! Check my work! 1. Find the area for the following figure. (trapazoid: bottom base 16.3, top base 5.9, height 4.6) 51.06 m^2*** 74.98 m^2 27.14 m^2 102.12 m^2 2. Find the area for the following figure. (1 point)

2. ### Algebra

How do you find the area of a shaded area in a triangle and assume the area of the largest triangle is one unit? If the largest (outer) triangle has area =1, and it has a base length b and height h, then (1/2) b h = 1 bh = 2 Then

3. ### math

Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 10 and its height is 6

4. ### math

The base of a triangle is four times its height. If the area of the triangle is 242 square millimeters, find its base and height.

1. ### Algebra

Write a function rule for the area A of a triangle whose base, b is 2 cm less than seven times the height, h. What is the area of the triangle when the height is 14 cm? is it A=7h^2 - 2h / 2 ?? a = 672 cm

2. ### Algebra

The height of a triangle is 8 m more than twice the length of the base. The area of the triangle is 32 m^2. Whats the height of the triangle

3. ### geometry

the area of a triangle is 27 square feet. its height is three times the length of its base. find the height and base of the triangle. i am unsure of how to set it up, please help

4. ### mathh

A right triangle has a height 8 cm more than twice the length of the base. If the area of the triangle is 96 cm2, what are the dimensions of the triangle.