Right Triangle: If m(A) = 60 Degrees, m(D) = 45 Degrees, BD = 15sqrt(2), find |AB|.

[kampoz13]

Sorry if the image is too low quality.

The question reads:
Right triangles ABC and BCD with right angle C are given below. If m(A) = 60 Degrees, m(D) = 45 Degrees, and BD = 15sqrt(2), find the length of AB.

I got an answer of 30, but for some reason I did not see it in the answer choices. Did I do something wrong? Thank you.

 

[Deleted member 4993]

Sorry if the image is too low quality.

The question reads:
Right triangles ABC and BCD with right angle C are given below. If m(A) = 60 Degrees, m(D) = 45 Degrees, and BD = 15sqrt(2), find the length of AB.

I got an answer of 30, but for some reason I did not see it in the answer choices. Did I do something wrong? Thank you.

Since we cannot see your work, we cannot tell if you had made mistakes.

By the way, there is a choice of "none of the above".

 

[Harry_the_cat]

Since we cannot see your work, we cannot tell if you had made mistakes.

By the way, there is a choice of "none of the above".

30 is incorrect. The correct answer is one of the options. Show how you got 30 and I'll point out your error.

 

[Deleted member 4993]

Sorry if the image is too low quality.

The question reads:
Right triangles ABC and BCD with right angle C are given below. If m(A) = 60 Degrees, m(D) = 45 Degrees, and BD = 15sqrt(2), find the length of AB.

I got an answer of 30, but for some reason I did not see it in the answer choices. Did I do something wrong? Thank you.

Remember the figure may not be drawn to scale.

BC = BD * sin(BDC)

AB = BC/sin(BAC)

continue.

If you still don't get the correct answer - come back showing your work.

 

[kampoz13]

Remember the figure may not be drawn to scale.

BC = BD * sin(BDC)

AB = BC/sin(BAC)

continue.

If you still don't get the correct answer - come back showing your work.

From what I know, BCD is a 45, 45, 90 degree right triangle. Therefore, it has a ratio of "a:a:a(sqrt(2))" where both legs are "a" and the hypothenuse is "a(sqrt(2)). Since BD is given to be 15sqrt(2), 15 should equal to "a". Meaning that both legs of triangle BCD are 15.

I then looked at triangle ABC and noticed it was a 30, 60, 90 degree right triangle. This triangle has a ratio of "a:a(sqrt(3)):2a" where "a" is equal to the shorter side of the triangle, 2a is the hypothenuse, and a(sqrt(3)) is the longer side. Since AB is the hypothenuse, which is also 2a, I multiplied 15 (since BC is 15 which is also "a") times 2 and gave me 30.

Hopefully that makes some sort of sense. Thank you.

Edit:
This triangle has a ratio of "a:a(sqrt(2)):2a"
to
"a:a(sqrt(3)):2a"
Typo.

 

[stapel]

From what I know, BCD is a 45, 45, 90 degree right triangle. Therefore, it has a ratio of "a:a:a(sqrt(2))" where both legs are "a" and the hypothenuse is "a(sqrt(2)). Since BD is given to be 15sqrt(2), 15 should equal to "a". Meaning that both legs of triangle BCD are 15.

I then looked at triangle ABC and noticed it was a 30, 60, 90 degree right triangle. This triangle has a ratio of "a:a(sqrt(2)):2a" where "a" is equal to the shorter side of the triangle, 2a is the hypothenuse, and a(sqrt(3)) is the longer side. Since AB is the hypothenuse, which is also 2a, I multiplied 15 (since BC is 15 which is also "a") times 2 and gave me 30.

This is exactly where the error is occurring, not because the statement is incorrect, but because you're letting the drawing fool you. Instead, use this:

more to scale:
        B
        *.
       /| \.
      / |   \.
     /  |     \.
    /   |       \.
   /    |         \.
  /     |           \.
 /      |             \
*-------*--------------*
A       C              D

Can you "see" better, from the above, how to apply the ratio? :wink:

 

[Ishuda]

From what I know, BCD is a 45, 45, 90 degree right triangle. Therefore, it has a ratio of "a:a:a(sqrt(2))" where both legs are "a" and the hypothenuse is "a(sqrt(2)). Since BD is given to be 15sqrt(2), 15 should equal to "a". Meaning that both legs of triangle BCD are 15.

I then looked at triangle ABC and noticed it was a 30, 60, 90 degree right triangle. This triangle has a ratio of "a:a(sqrt(2)):2a" where "a" is equal to the shorter side of the triangle, 2a is the hypothenuse, and a(sqrt(3)) is the longer side. Since AB is the hypothenuse, which is also 2a, I multiplied 15 (since BC is 15 which is also "a") times 2 and gave me 30.

Hopefully that makes some sort of sense. Thank you.

A 30, 60, 90 triangle has ratios of a:a sqrt(3):2 a

 

[kampoz13]

This is exactly where the error is occurring, not because the statement is incorrect, but because you're letting the drawing fool you. Instead, use this:

more to scale:
        B
        *.
       /| \.
      / |   \.
     /  |     \.
    /   |       \.
   /    |         \.
  /     |           \.
 /      |             \
*-------*--------------*
A       C              D

Can you "see" better, from the above, how to apply the ratio? :wink:

Ah. Ok. I reapplied the ratio and got 10sqrt(3). What I'm not understanding now is how should I know that AC is shorter than BC? Or do I even need the drawing at all?

 

[stapel]

What I'm not understanding now is how should I know that AC is shorter than BC? Or do I even need the drawing at all?

The bigger angle gets the bigger side opposite it, and the smaller angle gets the smaller side opposite it.

 

[kampoz13]

The bigger angle gets the bigger side opposite it, and the smaller angle gets the smaller side opposite it.

Ah. Thank you kind sir. c: