High School

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What is the measure of angel A rounded to nearest whole number ?


A. 30 degrees

B. 28 degrees

C. 2 degrees

D. 62 degrees

What is the measure of angel A rounded to nearest whole number A 30 degrees B 28 degrees C 2 degrees D 62 degrees

Answer :

Answer:

D. 62 degrees

Step-by-step explanation:

Here, ABC is a right angles triangle,

In which,

AB = 8 units,

AC = 17 units,

∠B = 90°,

By the pythogorous theorem,

[tex]AC^2=AB^2+BC^2[/tex]

[tex]17^2=8^2+BC^2[/tex]

[tex]289=64-BC^2[/tex]

[tex]225=BC^2[/tex]

[tex]\implies BC=15\text{ unit}[/tex]

By the law of sine,

[tex]\frac{sin A}{BC}=\frac{sin B}{AC}[/tex]

[tex]\frac{sin A}{15}=\frac{sin 90^{\circ}}{17}[/tex]

[tex]sin A = \frac{15}{17}[/tex]

[tex]\implies A= 61.9275^{\circ}\approx 62^{\circ}[/tex]

Hence, the measure of angle A is 62 degrees,

Option D is correct.

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Rewritten by : Barada

Use inverse cosine here because you have the side adjacent to angle A and the hypotenuse. On your calculator, press the 2nd key then cosine to see this on your display [tex] cos^{-1} [/tex] then enter 8/17 to give you an angle measure of 62 degrees.