To find the missing angle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the missing angle as angle A. Since one side is 97 and the bottom one is 192, we can set up the following equation:
97^2 + 192^2 = hypotenuse^2
9409 + 36864 = hypotenuse^2
46273 = hypotenuse^2
hypotenuse = √46273
hypotenuse ≈ 214.8
Now, we can find the sine of angle A:
sin(A) = opposite/hypotenuse
sin(A) = 192/214.8
sin(A) ≈ 0.8939
To find angle A, we can use the inverse sine function (sin^(-1)):
A = sin^(-1)(0.8939)
A ≈ 64.85 degrees
Therefore, the missing angle A is approximately 64.85 degrees.
finding a missing angle when one side is 97 and the bottom one is 192
3 answers
the pic is like and arrow some what straigth then a vertex then another arrow coming from that and one side of it is 97 and the bottom is 192. hope this makes sense
Thank you for the clarification. Based on your description, it sounds like you're referring to an isosceles triangle with the given side lengths of 97 and 192.
In an isosceles triangle, the two equal sides are opposite angles that are congruent. So in this case, the angle at the vertex (the top angle between the two arrows) can be bisected into two equal angles.
To find the measure of the top angle (let's call it angle A), we can first find the angle bisected by the base (the bottom side of length 192). This angle can be calculated using the inverse cosine function as follows:
cos(Angle bisected by base) = adjacent/hypotenuse
cos(Angle bisected by base) = 97/192
Angle bisected by base = cos^(-1)(97/192)
Angle bisected by base ≈ 57.99 degrees
Since this angle is bisected, the top angle (angle A) is twice this measure:
Angle A = 2 * 57.99
Angle A ≈ 115.98 degrees
Therefore, the missing angle at the vertex of the isosceles triangle is approximately 115.98 degrees.
In an isosceles triangle, the two equal sides are opposite angles that are congruent. So in this case, the angle at the vertex (the top angle between the two arrows) can be bisected into two equal angles.
To find the measure of the top angle (let's call it angle A), we can first find the angle bisected by the base (the bottom side of length 192). This angle can be calculated using the inverse cosine function as follows:
cos(Angle bisected by base) = adjacent/hypotenuse
cos(Angle bisected by base) = 97/192
Angle bisected by base = cos^(-1)(97/192)
Angle bisected by base ≈ 57.99 degrees
Since this angle is bisected, the top angle (angle A) is twice this measure:
Angle A = 2 * 57.99
Angle A ≈ 115.98 degrees
Therefore, the missing angle at the vertex of the isosceles triangle is approximately 115.98 degrees.