Evaluate the following trigonometric expression
1 answer:
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Pythagoras's theorem provides a simplification of thee relationship between the sides of a right triangle
- The length of the screen is <u>8 cm</u>
- The width of the screen is <u>6 cm</u>
<u />
Reason:
Known parameters:
Length of the diagonal of the television picture, d = 10 cm
Television screen viewing area, A = 48 cm²
Required:
To find the <em>length </em>and <em>width</em> of the screen
Solution:
Let, <em>L</em>, represent the length of the screen, and let <em>W</em> represent the width of the screen
Considering the right triangle formed by the length, <em>L</em>, the width, <em>W</em>, and a line along the diagonal, <em>d, </em> according to <em>Pythagoras's theorem</em>, we have;
d² = L² + W²
The equation for the area of the screen is A = L × W
Plugging in the known values into the two equations above gives;
10² = L² + W²...(1)
48 = L × W...(2)
From equation (2), we have;
...(3)
By substituting the expression for <em>W</em> in equation (3) above into equation (1) gives;
10²·L² = 48² + L²⁺² = 48² + (L²)²
Let <em>X</em> represent <em>L²</em>, we get;
X = L²
10²·X = 48² + X²
X² - 10²·X + 48² = 0
(X - 64)·(X - 36) = 0
∴ X = L² = 64 or 36
- L = √64 = 8, or L = √36 = 6
The longest side is the length, therefore, the length of the screen, L = <u>8 cm</u>
<u />
From , and L = 8, we have;
.
The width of the screen, W = <u>6 cm</u>
Learn more about Pythagoras's theorem here: