Destroyer Math Test 6 Q 16. 2013

[flossit]

The artist just finished a painting on canvas in the shape of right triangle. The lengths of the two longest sides of the painting are 23 and 14", and they meet at an angle of 55^.
Can someone explain? I thought when we have hypothenuse and adjacent and angle we use - CAH - 7 23 cos55?

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[DAT Destroyer]

The artist just finished a painting on canvas in the shape of right triangle. The lengths of the two longest sides of the painting are 23 and 14", and they meet at an angle of 55^.
Can someone explain? I thought when we have hypothenuse and adjacent and angle we use - CAH - 7 23 cos55?

You're right, but here we are looking for the opposite side which is the base, hence we used sin(55).
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[flossit]

Sorry but I still do not understand why I cannot use cos if I turned the triangle this way I draw on the picture that is attached. How do I know which side is being asked for? Can you please explain in which situations we use which Soh Cah Toa?

 

[Crithu]

View attachment 212770
Sorry but I still do not understand why I cannot use cos if I turned the triangle this way I draw on the picture that is attached. How do I know which side is being asked for? Can you please explain in which situations we use which Soh Cah Toa?

If you are looking for the area, it is easiest to take the two sides connected at the right triangle (not the hypotenuse) , so that you don't have to calculate the height from the hypotenuse to the right angle. Therefore, you have to find the missing side length.

You can use cos like your suggesting, but the angle you would be talking about would be the bottom right in your second triangle. This is the angle that gives you the unknown side as the adjacent side.

This new angle is 35 degrees and not 55 degrees. That should fix your problem.

 

[flossit]

If you are looking for the area, it is easiest to take the two sides connected at the right triangle (not the hypotenuse) , so that you don't have to calculate the height from the hypotenuse to the right angle. Therefore, you have to find the missing side length.

You can use cos like your suggesting, but the angle you would be talking about would be the bottom right in your second triangle. This is the angle that gives you the unknown side as the adjacent side.

This new angle is 35 degrees and not 55 degrees. That should fix your problem.

I'm now even more confused. Can you draw please?

 

[Crithu]

I'm now even more confused. Can you draw please?

The first picture shows the two possible ways to solve the area of this triangle. The first way is the way that we are solving, the second is the other possible way. As you can see, we have to solve for an unknown side either way we decide to solve (the second way would take an extra step).

The second picture is actually solving the problem. The 55 degree angle is located between 14 (a side) and 23 (hypotenuse). Using this angle, side 14 is the adjacent side. Our unknown side X is adjacent to angle θ. We find this unknown angle by subtracting the two known angles (90 and 55) from 180. This gives us 35 for angle θ. Now you can solve using cos.

However, this makes you go through the extra work of finding angle theta. If we just use the known angle, we can use sin to find the unknown side and skip this extra step (as @orgoman22 showed).

Hope this helps and let me know if you have any questions.

 

[flossit]

The first picture shows the two possible ways to solve the area of this triangle. The first way is the way that we are solving, the second is the other possible way. As you can see, we have to solve for an unknown side either way we decide to solve (the second way would take an extra step).

The second picture is actually solving the problem. The 55 degree angle is located between 14 (a side) and 23 (hypotenuse). Using this angle, side 14 is the adjacent side. Our unknown side X is adjacent to angle θ. We find this unknown angle by subtracting the two known angles (90 and 55) from 180. This gives us 35 for angle θ. Now you can solve using cos.

However, this makes you go through the extra work of finding angle theta. If we just use the known angle, we can use sin to find the unknown side and skip this extra step (as @orgoman22 showed).

Hope this helps and let me know if you have any questions.

Thank you! Now clear!