How Can You Solve a Triangle Using the Law of Sines Without a Calculator?

In summary, in Triangle ABC, when tan A=3/4 and tan B=1, and a=10, the measure of angle B is 45 degrees and sinA can be calculated by dividing the opposite side of angle A by the hypotenuse, which would be 3 divided by the square root of 3^2+4^2, resulting in sinA=3/5. Using this information, b can be calculated by using the equation sina/A=sinb/B and rearranging it to solve for b, which gives b=11.8 when using a calculator. However, it is possible to solve for b without using a calculator by using the known values of tanA and sinA to find the
  • #1
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Homework Statement


In Triangle ABC, tan A=3/4, tan B=1, and a=10. Find what b equals.


Homework Equations


You can use sina/A=sinb/B


The Attempt at a Solution


This problem is really easy using inv tangent functions and what not, but my teacher said we should be able to get it without a calculator.
Doing it with a calculator b will turn out to be 11.8. But if anyone is able to provide a detailed way to get the problem without using a calculator, that would be great.

Thanks
 
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  • #2
If tanB = 1, what's the measure of angle B? That's an easy one, and one that you should know. Also, if tanA = 3/4, it's pretty easy to get sinA.
 
  • #3
well the tanB=1 is equal to 45 degrees, but how can you get sinA from tanA?
 
  • #4
If tanB = 1, then B is 45 degrees - that's what you meant, right?

You have tanA = 3/4. Draw a right triangle and label the side opposite to A as 3 and the side adjacent to A as 4. What does the hypotenuse have to be? From that, what's sinA?
 

FAQ: How Can You Solve a Triangle Using the Law of Sines Without a Calculator?

1. What is the Law of Sines?

The Law of Sines is a mathematical rule that relates the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all sides and angles in a given triangle.

2. When do I use the Law of Sines?

The Law of Sines is used to solve triangles that have an angle-side-angle (ASA) or angle-angle-side (AAS) configuration. It is especially useful when you are given two angles and a side or two sides and a non-included angle in a triangle.

3. What information do I need to solve a triangle using the Law of Sines?

You need to know at least one angle and its opposite side or two sides and a non-included angle in order to use the Law of Sines. It is also helpful to have a calculator or trigonometric tables to find the sine of an angle.

4. How do I solve a triangle using the Law of Sines?

To solve a triangle using the Law of Sines, you will need to set up and solve a proportion with the given information. The proportion will have two sides and their corresponding angles, and the value of the sine of the known angle. Once you have solved for the unknown side or angle, you can use the Law of Sines again to find any remaining sides or angles.

5. Can the Law of Sines be used to solve any triangle?

No, the Law of Sines can only be used to solve triangles that have an angle-side-angle (ASA) or angle-angle-side (AAS) configuration. It cannot be used to solve triangles that have a side-side-angle (SSA) configuration, as this can result in two possible triangles with the given information.

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