Question

find x.
45
46.

1. problem solving find the value of x in the figure at the right.

Explanation:

Step1: Find top segment length

Let the vertical segment be $y$. Use Pythagoras:
$$y^2 + 7.5^2 = 11.6^2$$
$$y^2 = 11.6^2 - 7.5^2 = 134.56 - 56.25 = 78.31$$

Step2: Find right slant side length

Let the right slant side be $z$. Use Pythagoras:
$$z^2 = y^2 + 15^2 = 78.31 + 225 = 303.31$$

Step3: Solve for x using Pythagoras

For the small right triangle:
$$x^2 + 2.7^2 = z^2$$
$$x^2 = 303.31 - 7.29 = 296.02$$
$$x = \sqrt{296.02}$$

Step1: Apply Pythagorean theorem

$$8^2 + (x-4)^2 = x^2$$

Step2: Expand and simplify

$$64 + x^2 - 8x + 16 = x^2$$
$$80 - 8x = 0$$
$$8x = 80$$

Step1: Apply Pythagorean theorem

$$9^2 + (x-3)^2 = x^2$$

Step2: Expand and simplify

$$81 + x^2 - 6x + 9 = x^2$$
$$90 - 6x = 0$$
$$6x = 90$$

Answer:

$x \approx 17.21$

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For problem 45: