Question

PLEASE HELP! Find missing side lengths of B and C. Explain

Answer 1

b=7 & c=7√2

Explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer 2

• b = 7
• c = 7√2

Explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

Isosceles right triangle

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

c = 7√2

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Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

c² = 7² + b²

c² = 7² +7² = 2·7²

c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.