a triangular shelf is to be placed in a curio cabinet whose sides meet at an angle of 105 degrees. If the edges of the shelf along the sides measures 56 centimeters and 65 centimeters, how long is the outside edge of the shelf? Round to the nearest tenth.

Question

a triangular shelf is to be placed in a curio cabinet whose sides meet at an angle of 105 degrees. If the edges of the shelf along the sides measures 56 centimeters and 65 centimeters, how long is the outside edge of the shelf? Round to the nearest tenth.

Thanks for any help--I stink at word problems!

Answer 1

Suppose you laid the triangle down in front of you.

What would you see?

Would it not be a simple triangle with sides 56 and 65, and the angle contained between those two sides of 105º ?

clearly a Cosine Law question.

x^2 = 56^2 + 65^2 - 2(56)(65)cos 105º

solve for x

let me know what you got.

Answer 2

no, I got 96.15

x^2 = 56^2 + 65^2 - 2(56)(65)cos 105º
= 3136 + 4225 - 7280(-.258819)

notice the last term will become positive, I think you subtracted it instead.

Answer 3

x^2=3136+4225-(0.2588)

x^2=3136+4225+0.2588

x^2=7361.26

x=85.8

Answer 4

No ! your forgot an entire factor.

yours: x^2=3136+4225+0.2588
mine: x^2 = = 3136 + 4225 - 7280(-.258819)

Answer 5

Try again--

x^2=3136+4225-7280(-0.2588)

x^2=9245.06

x=96.2 cm

Answer 6

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c and angle C opposite side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we have a triangle with sides of 56 cm and 65 cm, and the angle between them is 105 degrees. Let's label the sides as follows:

a = 56 cm
b = 65 cm
C = 105 degrees

Now we can use the Law of Cosines to find the length of the outside edge, which we'll call "c."

c^2 = a^2 + b^2 - 2ab * cos(C)
c^2 = 56^2 + 65^2 - 2(56)(65) * cos(105)

Now we can calculate the value of c^2:

c^2 = 3136 + 4225 - 2(3640) * cos(105)

Next, we need to calculate cos(105) in order to simplify the equation further. To do that, we can use a calculator:

cos(105) ≈ -0.2588

Now we can substitute the value of cos(105) into the equation:

c^2 = 3136 + 4225 - 2(3640) * (-0.2588)
c^2 = 7456 + 3631
c^2 = 11087

Taking the square root of both sides, we get:

c ≈ √11087
c ≈ 105.3 cm

Therefore, the length of the outside edge of the shelf, rounded to the nearest tenth, is approximately 105.3 cm.

a triangular shelf is to be placed in a curio cabinet whose sides meet at an angle of 105 degrees. If the edges of the shelf along the sides measures 56 centimeters and 65 centimeters, how long is the outside edge of the shelf? Round to the nearest tenth.

Suppose you laid the triangle down in front of you.

x=95.5 cm

no, I got 96.15

x^2=3136+4225-(0.2588)

No ! your forgot an entire factor.

Try again--

To solve this problem, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c and angle C opposite side c, the following equation holds true: