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AleksAgata [21]
3 years ago
9

Solve for the right triangle given only one side and angle

Mathematics
2 answers:
34kurt3 years ago
8 0

Answer:

CD = √11 and CE = √11

Step-by-step 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.

sdas [7]3 years ago
5 0

Answer:

\huge \boxed{CD =\sqrt{11} } \\ \\ \huge \boxed{CE =\sqrt{11} }

Step-by-step explanation:

The triangle is a right triangle.

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

sin θ  = opp/hyp

sin 45 = <em>CD </em>/√22

Multiply both sides by √22.

√22 sin 45 = <em>CD</em>

√11 = <em>CD</em>

<em />

<em />

cos θ = adj/hyp

cos 45 = <em>CE</em> /√22

Multiply both sides by √22.

√22 cos 45 = <em>CE</em>

√11 = <em>CE</em>

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