Find each angle B. Do not use a calculator.

&...

Question

Find each angle B. Do not use a calculator.

Accepted Answer

Welcome back. Everyone in this problem, we want to determine the measure of angle B in the given figure. For our answer choices A says it's 45 degrees B, 90 degrees C, 30 degrees and D 60 degrees. Now, first of all, we know, we realize that angle B is right at the point B in our triangle. OK. And for typical naming convention, when working with triangles, let's call the side opposite to angle BB, the side opposite to angle A common A and the side opposite to angle C are common C. OK. Now, what do we know about our triangle that can help us to figure out angle B? Well, notice in our triangle, we have a pair of known side and unknown angle and opposite to angle B is the side AC which is six units. Now, if we have a known pair of angles and sides and we want to use it to help us find an unknown angle from another pair, what do we know that can help us? Well, we can recall the sign law. OK. And recall that the sign law tells us that for any triangle, the ratio of the sine of an angle to its opposite side is the same throughout the entire triangle. So basically what the sine law tells us is that the sine of angle A to A is going to be the same as the sine of angle B to B, which is going to be the same as the sine of angle C, the side C. OK. So here from our triangle, we want to figure out side B OK? And we already know the sine. Well, we already know the value of C and the length of side C. So we can use both of those to help us figure out the value of an B because by applying the sine law, then we're saying that the sine of B, the ratio of the sine of B to its opposite side six units is going to be the same as the ratio of the sine of C which is 60 degrees to its opposite side, which is three multiplied by the square root of six. So with this idea, we have one equation, one unknown we can solve for angle B. Now first let's multiply through by, by, by six units. OK. So when you multiply both sides by six, we get sine B to be equal to six multiplied by sine 60 degrees divided by three multiplied by the square root of six. No, if we put this into our calculator, if we were at the salt, OK, we should find that we get the sine of B to be equal to one divided by the square root of two. So to figure out B, we just need to find what that would be to give us a value of one divided by the spirit of two. Now, if the sine of B is this value, that means B is going to be equal to the inverse sine of that value. So in other words, B equals the inverse sine of one divided by the square root of two. Again, when we put this into our calculator, we should find that B equals 45 degrees. Therefore, angle B is 45 degrees A is the correct answer. Thanks for watching everyone. I hope this video helped.

Find each angle B. Do not use a calculator.

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Key Concepts

Trigonometric Ratios

Inverse Trigonometric Functions

Angle Relationships in Triangles

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