High School Math : How to find an angle in a right triangle
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Example Questions
Example Question #1 :How To Find An Angle In A Right Triangle
Acute angles x and y are inside a right triangle. If x is four less than one third of 21, what is y?
87
3
90
18
7
87
We know that the sum of all the angles must be 180 and we already know one angle is 90, leaving the sum of x and y to be 90.
Solve for x to find y.
One third of 21 is 7. Four less than 7 is 3. So if angle x is 3 then that leaves 87 for angle y.
例子问题# 21:Geometry
If a right triangle has one leg with a length of 4 and a hypotenuse with a length of 8, what is the measure of the angle between the hypotenuse and its other leg?
65
90
45
60
30
30
The first thing to notice is that this is a 30o:60o:90otriangle. If you draw a diagram, it is easier to see that the angle that is asked for corresponds to the side with a length of 4. This will be the smallest angle. The correct answer is 30.
Example Question #3 :Triangles
In the figure above, what is the positive difference, in degrees, between the measures of angleACBand angleCBD?
20
10
40
30
50
10
In the figure above, angleADBis a right angle. Because sideACis a straight line, angleCDBmust also be a right angle.
Let’s examine triangleADB. The sum of the measures of the three angles must be 180 degrees, and we know that angleADBmust be 90 degrees, since it is a right angle. We can now set up the following equation.
x+y+ 90 = 180
Subtract 90 from both sides.
x+y= 90
Next, we will look at triangleCDB. We know that angleCDBis also 90 degrees, so we will write the following equation:
y– 10 + 2x– 20 + 90 = 180
y+ 2x+ 60 = 180
Subtract 60 from both sides.
y+ 2x= 120
We have a system of equations consisting ofx+y= 90 andy+ 2x= 120. We can solve this system by solving one equation in terms ofxand then substituting this value into the second equation. Let’s solve foryin the equationx+y= 90.
x+y= 90
Subtractxfrom both sides.
y= 90 –x
Next, we can substitute 90 –xinto the equationy+ 2x= 120.
(90 –x) + 2x= 120
90 +x= 120
x= 120 – 90 = 30
x= 30
Sincey= 90 –x,y= 90 – 30 = 60.
The question ultimately asks us to find the positive difference between the measures ofACBandCBD. The measure ofACB= 2x– 20 = 2(30) – 20 = 40 degrees. The measure ofCBD=y– 10 = 60 – 10 = 50 degrees. The positive difference between 50 degrees and 40 degrees is 10.
The answer is 10.
Example Question #1 :How To Find An Angle In A Right Triangle
If angle
For this problem, remember that the sum of the degrees in a triangle is
That means that
Plug in our given values to solve:
Subtract
Example Question #4 :Triangles
Which of the following sets of line-segment lengths can form a triangle?
In any given triangle, the sum of any two sides is greater than the third. The incorrect answers have the sum of two sides equal to the third.
Example Question #1 :Right Triangles
In right
What is the value of
48
30
24
32
36
36
There are 180 degrees in every triangle. Since this triangle is a right triangle, one of the angles measures 90 degrees.
Therefore,
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