Trig Worksheet Finding X

If you're a student or teacher looking for practice problems in trigonometry to help improve your understanding of finding the value of x, then you've come to the right place. In this blog post, we will explore worksheets specifically designed to reinforce and hone your skills in this area.

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What is the value of x in a right triangle if the opposite side is length 5 and the adjacent side is length 12?

The value of x in a right triangle with an opposite side length of 5 and an adjacent side length of 12 can be found using the Pythagorean theorem. By squaring the lengths of the two sides and adding them together, we can find the square of the hypotenuse (x). Thus, x^2 = 5^2 + 12^2. Calculating this gives x^2 = 25 + 144 = 169. Therefore, x = ?169 = 13. Hence, the value of x in this right triangle is 13.

Determine the value of x in a right triangle if the hypotenuse measures 10 and the opposite side measures 8.

To determine the value of x in the right triangle, 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. So, x can be calculated as \( x = \sqrt{10^2 - 8^2} = \sqrt{100 - 64} = \sqrt{36} = 6 \). Therefore, the value of x in the right triangle is 6.

Find the value of x in a right triangle if the adjacent side is 16 and the hypotenuse is 20.

To find the value of x in a right triangle given that the adjacent side is 16 and the hypotenuse is 20, 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. So, we have 20^2 = 16^2 + x^2. Solving this equation, we get x = ?(20^2 - 16^2) = ?(400 - 256) = ?144 = 12. Therefore, the value of x in this right triangle is 12.

Calculate the value of x in a right triangle if the opposite side is 15 and the hypotenuse is 17.

To find the value of x in a right triangle where the opposite side is 15 and the hypotenuse is 17, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (17^2) is equal to the sum of the squares of the lengths of the other two sides (x^2 + 15^2). Therefore, x^2 + 15^2 = 17^2. Solving this equation will give us x = 8.

Determine the value of x in a right triangle if the opposite side is 20 and the adjacent side is 15.

To determine the value of x in a right triangle with an opposite side of 20 and an adjacent side of 15, you can use the Pythagorean theorem, which states that the square of the hypotenuse (x in this case) is equal to the sum of the squares of the other two sides. Therefore, x^2 = 15^2 + 20^2. This simplifies to x^2 = 225 + 400, x^2 = 625, and x = ?625, resulting in x = 25. Therefore, in this right triangle, the value of x is 25.

Find the value of x in a right triangle if the opposite side is 3 and the hypotenuse is 9.

To find the value of x in a right triangle where the opposite side is 3 and the hypotenuse is 9, you can use the Pythagorean theorem. In a right triangle, the square of the hypotenuse (9^2) is equal to the sum of the squares of the other two sides. So, 9^2 = x^2 + 3^2. This simplifies to 81 = x^2 + 9. Subtracting 9 from both sides gives x^2 = 72. Finally, taking the square root of both sides gives x = ?72 or x = 6?2. Thus, x is equal to 6?2 in this right triangle.

Calculate the value of x in a right triangle if the adjacent side is 10 and the hypotenuse measures 13.

Using the Pythagorean theorem (a^2 + b^2 = c^2), where a represents the adjacent side, b is the opposite side, and c is the hypotenuse, we can solve for the opposite side (x). Plugging in the given values, we have 10^2 + x^2 = 13^2. Simplifying this equation gives 100 + x^2 = 169. Subtracting 100 from both sides results in x^2 = 69. Taking the square root of both sides gives x = ?69, which simplifies to x ? 8.31 (rounded to two decimal places). Therefore, in this right triangle, the opposite side x is approximately 8.31 units long.

Determine the value of x in a right triangle if the opposite side is 6 and the adjacent side is 8.

To determine the value of x in a right triangle where the opposite side is 6 and the adjacent side is 8, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (x in this case) is equal to the sum of the squares of the other two sides. So, x^2 = 6^2 + 8^2, which simplifies to x^2 = 36 + 64, or x^2 = 100. Therefore, x = 10 in this right triangle.

Find the value of x in a right triangle if the opposite side is 9 and the hypotenuse is 15.

To find the value of x in a right triangle with an opposite side of 9 and a hypotenuse of 15, we can use the Pythagorean theorem. The formula is a^2 + b^2 = c^2, where a and b are the two sides of the triangle and c is the hypotenuse. Plugging in the values, we get 9^2 + x^2 = 15^2. Simplifying gives 81 + x^2 = 225. Subtracting 81 from both sides gives x^2 = 144. Taking the square root of both sides, we find x = 12. Therefore, the value of x in this right triangle is 12.

Calculate the value of x in a right triangle if the opposite side is 12 and the adjacent side is 5.

To find the value of x in a right triangle with an opposite side of 12 and an adjacent side of 5, you can use the Pythagorean theorem. The theorem states that the square of the hypotenuse (in this case, x) is equal to the sum of the squares of the other two sides (12^2 + 5^2). So, x^2 = 144 + 25 = 169. Taking the square root of 169 gives x = 13. Therefore, the value of x in this right triangle is 13.