Question
Let \( \angle D \) be an acute angle. Use a calculator to find \( m \angle D \) to the nearest tenth of a degree. \( \begin{array}{llll}\text { 3.) } \sin D=0.75 & \text { 4.) } \cos D=0.33 & \text { 5.) } \tan D=0.28\end{array} \)
Ask by Ortega Bryant. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
**3.) \( m \angle D \approx 48.6^\circ \)**
**4.) \( m \angle D \approx 70.7^\circ \)**
**5.) \( m \angle D \approx 15.6^\circ \)**
Solution
**3.) Calculate \( m \angle D \) when \(\sin D = 0.75\):**
We have
\[
D = \sin^{-1}(0.75).
\]
Using a calculator set to degrees, we find
\[
D \approx 48.6^\circ.
\]
---
**4.) Calculate \( m \angle D \) when \(\cos D = 0.33\):**
We have
\[
D = \cos^{-1}(0.33).
\]
Using a calculator set to degrees, we find
\[
D \approx 70.7^\circ.
\]
---
**5.) Calculate \( m \angle D \) when \(\tan D = 0.28\):**
We have
\[
D = \tan^{-1}(0.28).
\]
Using a calculator set to degrees, we find
\[
D \approx 15.6^\circ.
\]
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Simplify this solution The Deep Dive
To find the measure of angle \( D \) for each case, we can use the inverse trigonometric functions on a calculator. For \( \sin D = 0.75 \): Using the inverse sine function, we find: \[ D = \arcsin(0.75) \approx 48.6^\circ \] For \( \cos D = 0.33 \): Using the inverse cosine function, we find: \[ D = \arccos(0.33) \approx 70.8^\circ \] For \( \tan D = 0.28 \): Using the inverse tangent function, we find: \[ D = \arctan(0.28) \approx 15.7^\circ \] So, the measures of \( m \angle D \) to the nearest tenth of a degree are approximately: 1. \( 48.6^\circ \) 2. \( 70.8^\circ \) 3. \( 15.7^\circ \)
