The measure of one of the small angles of a right triangle is 26 more than 3 times the measure of the other small angle. Find the measure of both angles.
let the smallest angle be x
then the next smallest angle is 3x+26
You know in a right-angled triangle the two smaller angles must add up to 90° , so
x + 3x+26 = 90
solve for x ....
Well, it sounds like we've got a case of angle shenanigans in this right triangle! Let's break it down.
Let's call one of the small angles x, and the other small angle will be 3x + 26 (because it's 26 more than 3 times the measure of the other angle).
Since it's a right triangle, the sum of the two small angles should be equal to 90 degrees. That's just how right triangles roll.
So, we can set up an equation: x + (3x + 26) = 90.
Now, let's solve this equation to find the value of x.
4x + 26 = 90
Subtract 26 from both sides:
4x = 64
Divide both sides by 4:
x = 16
So, one small angle is 16 degrees, and the other small angle (3x + 26) would be:
3(16) + 26 = 48 + 26 = 74 degrees.
Therefore, one small angle is 16 degrees and the other small angle is 74 degrees, and together they form a right angle.
Let's assume that one of the small angles of the right triangle is x degrees.
According to the given information, the other small angle is 3x + 26 degrees.
The sum of all angles in a triangle is always 180 degrees.
In a right triangle, one angle is always 90 degrees.
So, the sum of the two small angles of the right triangle is (x) + (3x + 26) degrees.
According to the triangle angle sum property, this sum should be equal to 180 degrees.
Therefore, we can write the equation as:
x + (3x + 26) = 180
Now, let's solve this equation to find the value of x.
Combining like terms, we have:
4x + 26 = 180
Subtracting 26 from both sides, we have:
4x = 180 - 26
4x = 154
Dividing both sides by 4, we have:
x = 154/4
x = 38.5
So, one of the small angles is x = 38.5 degrees.
Now, let's find the value of the other small angle:
3x + 26 = 3(38.5) + 26
3x + 26 = 115.5 + 26
3x + 26 = 141.5
Therefore, the measure of the other small angle is 141.5 degrees.
In conclusion, one of the small angles of the right triangle is 38.5 degrees, and the other small angle is 141.5 degrees.
To solve this problem, let's assign variables to the unknown angles. Let x be the measure of one small angle and y be the measure of the other small angle.
From the information given in the question, we can set up two equations:
1) The sum of the two small angles in a triangle is 90 degrees, since it is a right triangle. Therefore, x + y = 90.
2) One of the angles is 26 more than 3 times the other angle. This can be written as an equation: x = 3y + 26.
Now, we have a system of two equations with two variables:
1) x + y = 90
2) x = 3y + 26
To solve this system, we can use the substitution method.
Step 1: Solve one of the equations for one variable. Let's solve the second equation for x in terms of y:
x = 3y + 26
Step 2: Substitute the expression of x from step 1 into the other equation. Substitute 3y + 26 for x in the first equation:
(3y + 26) + y = 90
Step 3: Simplify and solve for y:
4y + 26 = 90
4y = 90 - 26
4y = 64
y = 64/4
y = 16
Step 4: Substitute the value of y back into one of the original equations to find the value of x:
x + 16 = 90
x = 90 - 16
x = 74
Therefore, the measure of one small angle is 74 degrees and the measure of the other small angle is 16 degrees.