Math Problem Statement

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Solution

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Question 5

You are given a right-angled isosceles triangle with the right angle at AA. You need to find the value of tanB\tan B in this triangle.

For a right-angled isosceles triangle:

  • The two legs (sides opposite the angles AA and BB) are equal.
  • The angles opposite these sides are equal, each being 4545^\circ because the sum of the angles in a triangle is 180180^\circ.

Since tanB\tan B is the ratio of the opposite side to the adjacent side in a right triangle:

tanB=opposite side to Badjacent side to B=legleg=1\tan B = \frac{\text{opposite side to } B}{\text{adjacent side to } B} = \frac{\text{leg}}{\text{leg}} = 1

Question 6

You need to calculate 6×tan356 \times \tan 35^\circ to three decimal places.

Using a calculator:

tan350.7002\tan 35^\circ \approx 0.7002

So,

6×0.7002=4.20126 \times 0.7002 = 4.2012

Rounding to three decimal places:

6×tan354.2016 \times \tan 35^\circ \approx 4.201

Answers:

  1. Question 5: tanB=1\tan B = 1
  2. Question 6: 6×tan354.2016 \times \tan 35^\circ \approx 4.201

Would you like more details on these solutions or have any questions?

Here are five related questions you might explore:

  1. How do you calculate sinB\sin B in a right-angled isosceles triangle?
  2. What are the properties of an isosceles triangle?
  3. How does tan45\tan 45^\circ compare to tan30\tan 30^\circ and tan60\tan 60^\circ?
  4. What are the applications of trigonometric ratios in real-world problems?
  5. How do you convert degrees to radians in trigonometry?

Tip: Remember, for any right-angled isosceles triangle, the angles other than the right angle are always 4545^\circ.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Right-angled triangles
Isosceles triangles

Formulas

\( \tan \) ratio in a right triangle

Theorems

Properties of right-angled isosceles triangles

Suitable Grade Level

High school