Question

Can someone explain this to me

Answer 1

Answer:

10. x=10

11. x= 12

12. x= 8.944

13. x= 10.77

14. x= 12

15. x= 9.434

Step-by-step explanation:

There are a few methods of obtaining right triangle side lengths. Depending on what is given, you can use different relationships or laws to find the missing side:

Given two sides

If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:

a² + b² = c²

if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root:

a = √(c² - b²)

if leg b is unknown, then

b = √(c² - a²)

for hypotenuse c missing, the formula is

c = √(a² + b²)

Given angle and hypotenuse

Apply the law of sines or trigonometry to find the right triangle side lengths:

a = c * sin(α) or a = c * cos(β)

b = c * sin(β) or b = c * cos(α)

Given angle and one leg

Find the missing leg using trigonometric functions:

a = b * tan(α)

b = a * tan(β)

Given area and one leg

As we remember from basic triangle area formula, we can calculate the area by multiplying triangle height and base and dividing the result by two. A right triangle is a special case of a scalene triangle, in which one leg is the height when the second leg is the base, so the equation gets simplified to:

area = a * b / 2

For example, if we know only the right triangle area and the length of the leg a, we can derive the equation for other sides:

b = 2 * area / a

c = √(a² + (2 * area / a)²)