Find the area of the right triangle. If necessary, round to the nearest tenth.

A right triangle with side 15 yards and hypotenuse 25 yards.

a.

20 yd

b.

150 yd

c.

60 yd

d.

300 yd

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A right triangle with side 15 yards and hypotenuse 25 yards.

a.

20 yd

b.

150 yd

c.

60 yd

d.

300 yd

B. 150 yards

Step-by-step explanation:

Area of a Triangle = .5 * Base * height

So we need the height of the triangle, or the missing side.

We have to use Pythagorean Theorem to solve this:

A^2 + B^2 = C^2

15 ^ 2 + B ^ 2 = 25 ^2

b^2 = 25^2 - 15 ^ 2

b^2 = 625 - 225

b^2 = 400

sqrt (400) = 20

The missing height is 20. Now we plug it into 1/2 * b * H

.5 * 15 * 20

7.5 * 20 = 150

150 Yds

b

Step-by-step explanation:

Let's find the area of the adjacent side.

Applying Pythagoras' Theorem,

(adjacent side)²= 18² -9²

adjacent side[tex]= \sqrt{243}[/tex]

adjacent side= 15.588 m (5 s.f.)

Area of triangle= ½ ×base ×height

Area of traingle

[tex]= \frac{1}{2} \times15.588 \times 9 \\ = 70.1m \: (nearest \: tenth)[/tex]

The nearest answer is B.

*If you rounded of to the nearest tenth for the adjacent side first then use the formula for area of traingle, the result would be exactly 70.2 m.

B - 150 yd

Step-by-step explanation:

Obviously the first step is to find the missing measurement. To do this, you use the Pythagorean theorem; a² + b² = c².

In this case, let's label the the missing side A, the height B, and the hypotenuse C.

X² + 15² = 25²

Then you must figure out what 15² and 25².

15² = 225

25² = 625

The next step is to subtract 15² (225) from 25² (625), which will give you the result of X².

625 - 225 = 400.

Now you know X² = 400, you can find the square root of 400 to give you the length of the triangle.

√400 = 20.

The missing length of the triangle is 20 yards.

Now it's just a matter of finding the area by using the formula;

A = [tex]\frac{bh}{2}[/tex]

Or,

(20 × 15) ÷ 2 = 150.

And there's your answer. Don't forget to add the units.

Hope this helped.

a. 75 m

Step-by-step explanation:

Given,

Length of hypotenuse = 18m

Length of perpendicular = 10 m

To find:

Area of the right angled triangle

Formula to find area of the right angled triangle = [tex]\frac{perpendicular * base}{2}[/tex]

To find: Length of base

Hypotenuse² = Perpendicular² + Base²

Base² = Hypotenuse² - Perpendicular²

Base² = 18² - 10²

Base² = 324 - 100

Base² = 224

Base = [tex]\sqrt{224}[/tex]

Base = 14.97 m

Area of the right angled triangle = [tex]\frac{perpendicular * base}{2}[/tex]

⇒ [tex]\frac{10 * 14.87}{2}[/tex]

⇒ 74.85 m² or,

round to the nearest tenth = 75 m²