What are the values of a and b?
A right triangle is shown with a perpendicular segment drawn from the right angle to the opposite side.
The right triangle is formed by a left vertical leg and a lower horizontal leg. The third side connects the upper left to the lower right.
An inner segment is drawn from the right angle in the lower left to the third side so that the segment meets the third side at a right angle.
The left vertical leg is labeled 10.
The lower horizontal leg is labeled b.
The inner segment is labeled 6.
The segment from the upper left to the right angle intersection on the third side is labeled 8. The segment from the same intersection to the lower right is labeled a.
(1 point)
Responses
a=152, b=92
a=152, b=92
a=163, b=152
a=163, b=152
a=92, b=152
a=92, b=152
a=92, b=132
To find the values of a and b, we can use the Pythagorean Theorem.
Applying the Pythagorean Theorem to the inner segment and the vertical leg, we get:
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = 8
So, a = 8.
Applying the Pythagorean Theorem to the entire triangle, we get:
8^2 + b^2 = 10^2
64 + b^2 = 100
b^2 = 36
b = 6
So, b = 6.
Therefore, the values of a and b are a = 8 and b = 6.