QQuestionMathematics
QuestionMathematics
What is the length of the hypotenuse of the triangle?
| | | |
| --- | --- | --- |
| 7 cm | | |
| B | 3 cm | C |
| | | |
| 7 | 20 cm | |
| 0 | √23 cm | |
| 0 | √40 cm | |
| 0 | √58 cm | |
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:: Identify the given side lengths.
In the given triangle, we are provided with the lengths of two sides, 7 cm (labeled as the side adjacent to angle B) and 3 cm (labeled as the side opposite to angle B). We are asked to find the length of the hypotenuse (labeled as side c).
Step 2:: Apply the Pythagorean theorem.
c^2 = a^2 + b^2
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (side c) is equal to the sum of the squares of the lengths of the other two sides (sides a and b). In equation form, this can be written as:
Step 3:: Plug in the known side lengths.
c^2 = (7 \text{ cm})^2 + (3 \text{ cm})^2
Using the given side lengths, we can write:
Step 4:: Calculate the squares of the side lengths.
c^2 = 49 \text{ cm}^2 + 9 \text{ cm}^2
Step 5:: Add the squared side lengths.
c^2 = 58 \text{ cm}^2
Step 6:: Find the square root of both sides.
c = \sqrt{58 \text{ cm}^2}
To find the length of the hypotenuse, we need to take the square root of both sides of the equation:
Step 7:: Calculate the square root.
c \approx 7.62 \text{ cm}
Final Answer
The length of the hypotenuse is approximately 7.62 cm.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students