in a big right triangle with a small right triangle inside of it. C is the length of the whole thing., R is the adjacent of the small tri. H is the oopisite of the small tri. B is the adjacent of the big tri. as well as the hypotenuse of the small tri. S is the oppisite of the big triangle. and A is the hypotenuse of the big tri. how do you find H if R=3 and S = 6. what is it? How do you find R if C =18 and B=6. how do you find A if C = 12 and R = 3. PLEASE PLEASE HELP ME WITH THIS, I AM COMPLETELY STUMPED, I THINK IT HAS SOMETHING TO DO WITH PYTH. THEOREM, BUT I'M NOT SURE AND NEED AN ANSWER BEFORE TOMORROW.
can you draw a picture on paint? i can't understand your question.
i don't know how to do that. sorry.
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To solve these problems, you can indeed use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let me explain step by step how to find the missing side lengths in each scenario:
1. To find H in the first problem, you have the adjacent side R = 3 and the opposite side S = 6. Since H is the opposite side of the small right triangle, we can use the Pythagorean theorem: R^2 + H^2 = B^2. Plugging in the known values, we get 3^2 + H^2 = 6^2. Simplifying, we have 9 + H^2 = 36. Subtracting 9 from both sides, we get H^2 = 27. Finally, take the square root of both sides to find H. Rounded to two decimal places, H is approximately 5.20.
2. In the second problem, you are given C = 18 and B = 6. Since R is the adjacent side of the big triangle, and B is also the adjacent side of the small triangle, we can set up an equation using the Pythagorean theorem again: R^2 + B^2 = C^2. Substituting the given values, we get R^2 + 6^2 = 18^2. Simplifying, we have R^2 + 36 = 324. Subtracting 36 from both sides, we get R^2 = 288. Finally, take the square root of both sides to find R. Rounded to two decimal places, R is approximately 16.97.
3. In the third problem, you are given C = 12 and R = 3. This time, you need to find A, which is the hypotenuse of the big triangle. Since C is adjacent to the right angle and R is opposite to the right angle, we can set up the equation using the Pythagorean theorem: R^2 + A^2 = C^2. Substituting the given values, we get 3^2 + A^2 = 12^2. Simplifying, we have 9 + A^2 = 144. Subtracting 9 from both sides, we get A^2 = 135. Finally, take the square root of both sides to find A. Rounded to two decimal places, A is approximately 11.62.
Remember to double-check your work and use the appropriate units if necessary. If you come across any further questions, feel free to ask!