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Please solve for X! (may use Tan Sin and Cos- possibly the law of cosine??)

inside is 90 degrees then x then 40 then 30

Please solve for X! (may use Tan Sin and Cos- possibly the law of cosine??) inside-example-1
User AC At CA
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The value of x is approximately 25.84 degrees (using sin) or 70.14 degrees (using cos) .

The triangle is a right triangle, with one angle measuring 90 degrees. The other two acute angles are labelled as x and 40 degrees.

We can use the trigonometric ratios sine (sin), cosine (cos), and tangent (tan) to solve for x.

Here are two methods:

Method 1: Using sine (sin)

We know the length of the side opposite the angle x (let's call it a) and the length of the hypotenuse (let's call it c).

We can see from the image that a = 40 and c = 90.

We can use the definition of sin: sin(x) = a/c = 40/90 = 4/9.

Take the inverse sine (arcsin) of both sides to find x: x = arcsin(4/9).

Using a calculator, we get x ≈ 25.84 degrees.

Method 2: Using cosine (cos)

We know the length of the side adjacent to the angle x (let's call it b) and the length of the hypotenuse (c).

We can see from the image that b = 30 and c = 90.

We can use the definition of cos: cos(x) = b/c = 30/90 = 1/3.

Take the inverse cosine (arccos) of both sides to find x: x = arccos(1/3).

Using a calculator, we get x ≈ 70.14 degrees.

Therefore, the value of x is approximately 25.84 degrees (using sin) or 70.14 degrees (using cos).

User Linto Davis
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