Example Question - right triangle problem
Here are examples of questions we've helped users solve.
Solving a Right Triangle Problem with Trigonometry
This question involves using trigonometry to solve a right triangle problem. The information provided indicates that Franklin casts a 60° shadow, and the distance from the top of Franklin's head to the shadow's end is 7 feet. The question asks for the length of Franklin's shadow and his height. The 60° angle and the distance from Franklin's head to the shadow's end form a right triangle, with the 7 feet representing the hypotenuse. Let's denote the following: - \( h \) as Franklin's height, - \( s \) as the length of the shadow, - \( 60° \) as the angle of elevation from the end of the shadow to the top of Franklin's head. We can use trigonometry to solve for both \( s \) and \( h \). More specifically, the cosine and sine functions for a 60° angle in a right triangle. Using the cosine function, which is adjacent over hypotenuse: \[ \cos(60°) = \frac{s}{7} \] Since \( \cos(60°) = 0.5 \): \[ 0.5 = \frac{s}{7} \] \[ s = 7 \times 0.5 \] \[ s = 3.5 \text{ feet} \] Using the sine function, which is opposite over hypotenuse: \[ \sin(60°) = \frac{h}{7} \] Since \( \sin(60°) = \sqrt{3}/2 \) or approximately 0.8660: \[ 0.8660 = \frac{h}{7} \] \[ h = 7 \times 0.8660 \] \[ h \approx 6.0620 \text{ feet} \] Rounded to one decimal place, Franklin's height would be approximately 6.1 feet. So, the length of Franklin's shadow is 3.5 feet, and his height is approximately 6.1 feet. The correct answer from the options provided would be: A. 3.5 ft., 6.1 ft.
Solving Right Triangle with Pythagorean Theorem
这个问题是一个直角三角形的问题，我们要使用勾股定理来求解斜边AB的长度。勾股定理表示在直角三角形中，斜边的平方等于两个直角边的平方和。所以，我们可以表示为： AB² = AC² + BC² 已知AC = 2米，BC = 6米。我们可以把它们代入上面的公式： AB² = 2² + 6² AB² = 4 + 36 AB² = 40 然后，我们需要计算AB的值，即求平方根： AB = √40 AB = 2√10 (约为6.32米) 因此，直角三角形斜边AB的长度约为6.32米。
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