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Solve for the right triangle given only one side and angle

Solve for the right triangle given only one side and angle-example-1
User GeekMasher
by
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2 Answers

3 votes

Answer:


\huge \boxed{CD =√(11) } \\ \\ \huge \boxed{CE =√(11) }

Explanation:

The triangle is a right triangle.

We can apply trigonometric functions to solve for the missing sides.

sin θ = opp/hyp

sin 45 = CD /√22

Multiply both sides by √22.

√22 sin 45 = CD

√11 = CD

cos θ = adj/hyp

cos 45 = CE /√22

Multiply both sides by √22.

√22 cos 45 = CE

√11 = CE

User Bravohex
by
7.9k points
1 vote

Answer:

CD = √11 and CE = √11

Explanation:

We know that m∠D is 45° (by using the sum of interior angles in a triangle) so therefore, ΔDCE is a 45 - 45 - 90 triangle (the 45, 45, and 90 refer to the angle measures). The ratio of sides in a 45 - 45 - 90 triangle is 1 : 1 : √2 where the 1s are the sides and the √2 is the hypotenuse. We need to solve for x in x : x : √22. If you notice that √22 = √2 * √11, we can use this to find x, therefore, x = 1 * √11 = √11 so CD = √11 and CE = √11.

User Mehul Thakkar
by
7.8k points

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