I need help with this geometry question
1 answer:
Answer:
radius ≈ 15.5
Step-by-step explanation:
the radius is RS
the angle between a tangent and the radius at the point of contact is 90°
then Δ RST is a right triangle
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then
RS² + ST² = RT² ( substitute values )
RS² + 7² = 17²
RS² + 49 = 289 ( subtract 49 from both sides )
RS² = 240 ( take square root of both sides )
RS = ≈ 15.5 ( to 1 dec. place )
You might be interested in
Answer:
Leg side along the wall = x ft = 8 ft
The other leg side = 7+x ft = 7+8=15 ft
The Hypotenuse =9+x ft = 9+8 = 17 ft
Step-by-step explanation:
In the question, the shape of the pool is right triangle.
Let the leg side along the wall to be the x ft
Let the other leg side to be 7+x ft
Let the longest side/hypotenuse to be x+9 ft
Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse
This means;
Expand the terms in brackets
collect like terms
solve for x in the quadratic equation by factorization
Taking the positive value of x;
x=8ft
Finding the lengths
Leg side along the wall = x ft = 8 ft
The other leg side = 7+x ft = 7+8=15 ft
The Hypotenuse =9+x ft = 9+8 = 17 ft