Answer:
A = 42.5° (nearest tenth)
B = 47.5° (nearest tenth)
C = 90°
a = 11
b = 12
c = √(265) = 16.3 (nearest tenth)
Step-by-step explanation:
Information:
Side a is opposite angle A.
Side b is opposite angle B.
Side c is opposite angle C.
From inspection of the triangle:
To find the missing side length, use Pythagoras Theorem:
Pythagoras Theorem
a² + b² = c²
(where a and b are the legs and c is the hypotenuse of a right triangle).
Substitute the given values of a and b into the formula and solve for c:
⇒ 11² + 12² = c²
⇒ 121 + 144 = c²
⇒ c² = 265
⇒ c = √(265)
To find one of the missing angles, use the Sine Rule.
Sine Rule
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Substitute the given values into the formula:
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin B}{12}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]
Solve for angle A:
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{\sin 90^{\circ}}{\sqrt{265}}[/tex]
[tex]\implies \sf \dfrac{\sin A}{11}=\dfrac{1}{\sqrt{265}}[/tex]
[tex]\implies \sf \sin A=\dfrac{11}{\sqrt{265}}[/tex]
[tex]\implies \sf A=\sin^{-1} \left(\dfrac{11}{\sqrt{265}}\right)[/tex]
[tex]\implies \sf A=42.51044708...^{\circ}[/tex]
Therefore, A = 42.5° (nearest tenth)
Interior angles of a triangle sum to 180°:
⇒ A + B + C = 180°
⇒ 42.5° + B + 90° = 180°
⇒ B + 132.5° = 180°
⇒ B = 47.5°
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