ABC is a triangle such that AB = 84 and AC = 28. Let D be a point on the line segment BC, such that ∠CAD = ∠BAD = 60 ∘. What is the length of AD? I've tried drawing an altitude from the vertex B, just to form a right triangle EAB whom I figured out the lengths based on the sine and cosine of 60 ∘.
T angent of the angle = O pposite side length / A djacent side length $\tan θ = \frac {Opposite} {Adjacent}$ "Adjacent" meaning the side which the given angle joins to the hypotenuse (a if you use the angle 30°), and "Opposite" meaning the side that is not connected to the angle you are using for the calculation (a if you use the angle 60°).
Here are a few examples. Closing Remarks If you want to calculate the third side of the triangle, you need more information than simply two sides. For example, if you know the triangle is a right triangle, or if you know the measure of the included angle between the two known segments, then you can determine the length of the third side.
In the case of a general isosceles triangle, the angle bisector between the two equal sides is also an altitude/perpendicular to the third side. Thus this would divide the isosceles triangle into two right triangles, and if the length of the altitude is known, the third side's length can be found by an application of the Pythagorean formula.
Assume I have any triangle $\\triangle ABC$. I know that given the lengths two sides of the triangle and angle between them, I can find the length of the third side. In other words, given values of ...
2 Think about similar triangles. Two similar triangles have exactly the same angles, but the sides are (generally) not the same length. That fact alone tells you that it is not possible to determine the lengths of the sides of a triangle if all you know is the angles -- you have to also know at least one side length in order to fix the scale.
0 I would like to calculate the length of the side in red on the image. I tried the Law of cosines, but maybe i haven't applied the formula right, because for a side "a" and "b" of size 64 and a angle of 120, the result is 39. How to calculate the right length of c for the image?
Don’t calculate, cut the triangle along the height instead to get two triangles with sides $8-17-15$. Now glue them together at their common sides of length $8$ to get the wanted triangle; its sides are $17-17-30$.
Given the base and angles of an isosceles triangle, how to find length of the two sides? Ask Question Asked 12 years, 10 months ago Modified 1 year, 7 months ago
11 How do I prove that a triangle with sides a, b, c, has an angle bisector (bisecting angle A) is of length: 2√bcs(s − a) b + c I have tried using the sine and cosine rule but have largely failed. A few times I have found a way but they are way too messy to work with.
