SOLUTION: Suppose triangle LWT is isosceles, the measure of angle W= 90 degrees, LW= 7X+ 21, and TW= 4X + 21. a. Determine LW,TW,LT, the measure of angle L and angle T. from: geometry

Algebra ->  Algebra  -> Triangles -> SOLUTION: Suppose triangle LWT is isosceles, the measure of angle W= 90 degrees, LW= 7X+ 21, and TW= 4X + 21. a. Determine LW,TW,LT, the measure of angle L and angle T. from: geometry       Log On

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Question 164631This question is from textbook Geometry concepts and skills
: Suppose triangle LWT is isosceles, the measure of angle W= 90 degrees, LW= 7X+ 21, and TW= 4X + 21.
a. Determine LW,TW,LT, the measure of angle L and angle T.
from: geometry
concepts and skills
Chapter 4 Section 7
This question is from textbook Geometry concepts and skills

Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
isosceles means that the two base angles are equal as are the sides opposite the angles

LW=TW __ 7X+21=4X+21 __ subtracting 4x+21 __ 3X=0 __ X=0

LW=TW=21

there are 180º in a triangle __ the vertex angle is 90º, so the sum of the two base angles is also 90º
__ so each bse angle equals 45º

by Pythagoras __ LT^2=LW^2+TW^2 __ LT^2=2(21^2) __ LT=21*sqrt(2)