Question

Given circle E with diameter bar (CD) and radius bar (EA)*bar (AB) is tangent to E at A. If EA=11 and AB=16, solve for EB. Round your answer to the nearest tenth if necessary. If the answer cannot be

Answer 1

To find the length of EB, we use the Pythagorean theorem in the right triangle EAB, with EA=11 and AB=16. Upon calculation, we find that EB is approximately 19.4 units.

Step-by-step explanation:

The student has been asked to solve for EB in a geometry problem involving a circle with a diameter and a radius. Given that EA is the radius of circle E and AB is the tangent to circle E at point A, we can use the Pythagorean theorem to solve for the length of EB. Because EA is a radius and EB is a diameter, the triangle EAB is a right triangle, and we can use the lengths EA = 11 (radius) and AB = 16 (tangent) to find EB.

Using the Pythagorean theorem for right triangle EAB, we have:

EA2 + AB2 = EB2

112 + 162 = EB2

121 + 256 = EB2

377 = EB2

EB = √377

EB ≈ 19.4

The length of EB is approximately 19.4 units, rounded to the nearest tenth.