Precalculus : Solving Right Triangles
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Example Questions
Example Question #1 : Trigonometric Applications
In a right triangle, if the hypotenuse is 
Use the Pythagorean Theorem to find the other leg.
The length of the given leg is 3, and the unknown leg is 
Use the area of a triangle formula and solve.
Example Question #2 : Trigonometric Applications
An isosceles right triangle has a hypotenuse of 1. What is the area of this triangle?
Write the formula for the Pythagorean theorem.
In an isosceles right triangle, both legs of the right triangle are equal.
Substitute the either variable and the known hypotheuse and determine the side length.
This length represents both the base and the height of the triangle. Write the area of a triangle and substitute to solve for the area.
Example Question #1 : Solve A Right Triangle
Solve the right triangle.
C=90°
B=45°
a=5
c=
A=135°
b=2.07
None of these answers are correct.
A=45°
b=
A=45°
b=5
A=135°
b=5
A=45°
b=5
Given that:
C=90°
B=45°
a=5
c=
Therefore...
All angles of a triangle add up to 180°.
Example Question #4 : Solve A Right Triangle
A right triangle has a base of 10 and a hypotenuse of 20. What is the length of the other leg?
Write the Pythagorean Theorem.
Substitute the values of the leg and hypotenuse. The hypotenuse is the longest side of the right triangle. Solve for the unknown variable.
Example Question #1 : Solving Right Triangles
In the right triangle ABC, side AB is 
Given that ABC is a right triangle, the length of hypotenuse BC is the root of the sum of the squares of the two other sides (in other words, 
Example Question #1 : Trigonometric Applications
The side lengths of right triangle ABC are such that AC > BC > AB. AC = 25 and AB = 9. What is the length of BC?
When you are using Pythagorean Theorem to calculate the missing side of a right triangle, it is crucial that you identify which side is the hypotenuse, 
And then you can perform the calculations on the known values:
Meaning that:
From there you can simplify, arriving at a = 4 times the square root of 34.
Example Question #1 : Solve A Right Triangle
Given 
Since the angle of the isosceles is 
Using 
Then solve for 
Simplify: 
Lastly, round and add appropriate units: 
Example Question #1 : Solve A Right Triangle
In isosceles triangle 
In the diagram, AB is cut in half by the altitude.
From here it easy to use right triangle trigonometry to solve for AC.
Example Question #9 : Solve A Right Triangle
Find the area of the following Isosceles triangle (units are in cm):
The formula for the area of a triangle is:
We already know what the base is and we can find the height by dividing the isosceles triangle into 2 right triangles:
From there, we can use the Pathegorean Theorem to calculate height:
To find the area, now we just plug these values into the formula:
Example Question #10 : Solve A Right Triangle
Find the area of the given isosceles triangle and round all values to the nearest tenth:
The first step to solve for area is to divide the isosceles into two right triangles:
From there, we can determine the height and base needed for our area equation 
From there, height can be easily determined using the Pathegorean Theorem:
Now both values can be plugged into the Area formula:
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