I have a diagram of how far a discus was thrown.
From A to B is 100m, C is perpendicular to A, from A to C is 50m, A and B are connected to D (it should be a triangle), A has a 40° angle and B has a 75° angle. C is not perpendicular to D btw..
a. Find AD and use it to find CD.
*AD=107.33m, CD=84.38m is that correct?*
b. Find an expression for the distance from Point A to point D, in terms of α and β. Then use that to find and expression for CD, in terms of α and β.
Huh?? I'm confused, help me please!
AD/sin75° = 100/sin65°
AD = 106.58
CD^2 = 50^2 + 106.58^2 - 2*50*106.58 cos50°
CD = 83.72
Hmmm. we're close. Better check
(a) my math
(b) your math
On part b, ya got me. what are α and β supposed to be? Maybe they are to be substituted for the actual angles we used to compute the distances. Then the formula can be used for other angle values.
I double checked my math, and you're right.
For part b, they gave the same diagram except for angle A it's α instead of 40° and angle B is β.
Steve!!! Your grounded! I'm so glad I found this website you little piece of crap.
Sure! Let's break down the problem step by step.
a. To find AD, we can use the law of sines. The law of sines states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In triangle ABD, we have angle A = 40 degrees and angle B = 75 degrees. We know the length of AB is 100m.
Using the law of sines, we can set up the following equation:
sin(40°) / AB = sin(75°) / AD
Solving for AD, we have:
AD = AB * (sin(40°) / sin(75°))
AD = 100 * (sin(40°) / sin(75°))
AD ≈ 100 * (0.6428 / 0.9659)
AD ≈ 69.84m
So, the length of AD is approximately 69.84m.
To find CD, we can use the Pythagorean theorem. CD is the hypotenuse of triangle ACD, where AC = 50m and AD = 69.84m.
Using the Pythagorean theorem:
CD^2 = AC^2 + AD^2
CD^2 = 50^2 + 69.84^2
CD^2 ≈ 2500 + 4879.2656
CD^2 ≈ 7379.2656
CD ≈ √7379.2656
CD ≈ 85.83m
So, the length of CD is approximately 85.83m.
For validation, the values you provided (AD = 107.33m, CD = 84.38m) do not match the calculations I've shown above. Please double-check your calculations.
b. To find an expression for the distance from Point A to Point D in terms of α and β, we can use the law of sines again. Let x represent the length of AD.
Using the law of sines in triangle ABD:
sin(α) / AB = sin(β) / x
Rearranging the equation, we have:
x = AB * (sin(β) / sin(α))
Similarly, to find an expression for CD in terms of α and β, we can use the Pythagorean theorem in triangle ACD, with AD represented by x:
CD^2 = AC^2 + x^2
CD^2 = AC^2 + (AB * (sin(β) / sin(α)))^2
Simplifying, we get:
CD = √(AC^2 + (AB * (sin(β) / sin(α)))^2)
These expressions will give you a general formula to calculate the distances in terms of the angles α and β.