Question

kuta software - infinite geometry
inverse trigonometric ratios
find each angle measure to the nearest degree.

1. ( sin b = 0.4848 )
2. ( sin a = 0.5150 )
3. ( cos a = 0.7431 )
4. ( cos w = 0.6157 )
5. ( cos a = 0.5878 )
6. ( \tan w = 19.0811 )
7. ( cos a = 0.4226 )
8. ( \tan w = 0.5317 )

find the measure of the indicated angle to the nearest degree.
9)
10)
11)
12)
14)

Explanation:

Step1: Recall inverse trigonometric functions

For a right - triangle, if we know the ratio of the sides, we can use inverse trigonometric functions. The basic formulas are:

• If \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), then \(\theta = \sin^{- 1}(\frac{\text{opposite}}{\text{hypotenuse}})\)
• If \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), then \(\theta=\cos^{-1}(\frac{\text{adjacent}}{\text{hypotenuse}})\)
• If \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), then \(\theta=\tan^{-1}(\frac{\text{opposite}}{\text{adjacent}})\)

Step2: Solve for each angle

1. For \(\sin B = 0.4848\), \(B=\sin^{-1}(0.4848)\approx29^{\circ}\)
2. For \(\sin A=0.5150\), \(A = \sin^{-1}(0.5150)\approx31^{\circ}\)
3. For \(\cos A=0.7431\), \(A=\cos^{-1}(0.7431)\approx42^{\circ}\)
4. For \(\cos W = 0.6157\), \(W=\cos^{-1}(0.6157)\approx52^{\circ}\)
5. For \(\cos A=0.5878\), \(A=\cos^{-1}(0.5878)\approx54^{\circ}\)
6. For \(\tan W=19.0811\), \(W=\tan^{-1}(19.0811)\approx87^{\circ}\)
7. For \(\cos A=0.4226\), \(A=\cos^{-1}(0.4226)\approx65^{\circ}\)
8. For \(\tan W=0.5317\), \(W=\tan^{-1}(0.5317)\approx28^{\circ}\)
9. For the right - triangle with adjacent side \(a = 38\) and opposite side \(o=27\), \(\theta=\tan^{-1}(\frac{27}{38})\approx35^{\circ}\)
10. For the right - triangle with adjacent side \(a = 21\) and opposite side \(o = 9\), \(\theta=\tan^{-1}(\frac{9}{21})\approx23^{\circ}\)
11. For the right - triangle with adjacent side \(a=29\) and opposite side \(o = 14\), \(\theta=\tan^{-1}(\frac{14}{29})\approx26^{\circ}\)
12. For the right - triangle with adjacent side \(a = 40\) and hypotenuse \(h=42\), \(\theta=\cos^{-1}(\frac{40}{42})\approx14^{\circ}\)
13. For the right - triangle with opposite side \(o = 10\) and hypotenuse \(h = 39\), \(\theta=\sin^{-1}(\frac{10}{39})\approx15^{\circ}\)
14. For the right - triangle with opposite side \(o=11\) and hypotenuse \(h = 27\), \(\theta=\sin^{-1}(\frac{11}{27})\approx24^{\circ}\)

Answer:

1. \(29^{\circ}\)
2. \(31^{\circ}\)
3. \(42^{\circ}\)
4. \(52^{\circ}\)
5. \(54^{\circ}\)
6. \(87^{\circ}\)
7. \(65^{\circ}\)
8. \(28^{\circ}\)
9. \(35^{\circ}\)
10. \(23^{\circ}\)
11. \(26^{\circ}\)
12. \(14^{\circ}\)
13. \(15^{\circ}\)
14. \(24^{\circ}\)