An oblique triangle ABC has internal angles ∠A=40∘ and ∠B=53∘, and the length of the side opposite to ∠C is c=30 (metres). Determine the length of the side opposite to ∠A, denoted a, to 2 decimal places.
a=
Number
metres (2 decimal places).
Surely you must have found ∠C = 87°
Simple case of the sine law:
BC/sin40 = 30/sin87
BC = 30sin40/sin87 = ....
Hello. I dont understand question number 2 for the linear model part. this is the info i have:
burj khalifa
163 floors
2,717 feet
tokyo treehouse
29 floors
2080 feet
can you please solve or explain how to get the equasion.
To determine the length of the side opposite to angle A, denoted as side a, we can use the law of sines. The law of sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In this case, we have the following information:
∠A = 40°
∠B = 53°
Side opposite ∠C = c = 30 meters
To find side a, we can set up the following equation using the law of sines:
sin(∠A) / a = sin(∠C) / c
Since we are trying to solve for a, we rearrange the equation:
a = (c * sin(∠A)) / sin(∠C)
We can substitute the given values into the equation and calculate side a:
a = (30 * sin(40°)) / sin(∠C)
To find sin(∠C), we can use the fact that the sum of the angles in a triangle is 180°:
∠C = 180° - ∠A - ∠B
∠C = 180° - 40° - 53°
∠C = 87°
Now we have all the information we need to calculate side a:
a = (30 * sin(40°)) / sin(87°)
Using a calculator or trigonometric table, we can find the sine of 40° and 87° and substitute them into the equation to solve for a.
a ≈ (30 * 0.64278760968) / 0.99904822158
a ≈ 19.283628290187053
Therefore, the length of side a is approximately 19.28 meters.