Answer:
10. x=10
11. x= 12
12. x= 8.944
13. x= 10.77
14. x= 12
15. x= 9.434
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)