1. **Problem b:** Find the angle $\theta$ between the ground and the ladder given $\cos \theta = \frac{5}{20}$.\n\n2. **Formula:** Use the cosine inverse function to find the angle: $$\theta = \cos^{-1}\left(\frac{5}{20}\right)$$\n\n3. **Calculate:** Simplify the fraction: $$\frac{5}{20} = \frac{1}{4}$$\n\n4. **Evaluate:** $$\theta = \cos^{-1}\left(\frac{1}{4}\right) \approx 75.5^\circ$$\n\n5. **Find angle with ground:** Since the ladder forms a right angle with the wall, the angle between the ladder and the ground is $$90^\circ - 75.5^\circ = 14.5^\circ \approx 15^\circ$$\n\n---\n\n1. **Problem c:** Find how high a 16-foot ladder reaches up a wall when placed correctly on level ground, given the angle $\theta = 15^\circ$.\n\n2. **Formula:** Use the sine ratio for height: $$\sin \theta = \frac{\text{height}}{\text{ladder length}}$$\n\n3. **Calculate height:** $$\text{height} = 16 \times \sin 15^\circ$$\n\n4. **Evaluate:** $$\sin 15^\circ \approx 0.2588$$\n$$\text{height} = 16 \times 0.2588 = 4.14 \text{ feet}$$\n\n---\n\n1. **Problem d:** Find the angle $\theta$ to cut a 1.5" wide board so the cut length is 2".\n\n2. **Formula:** Use sine ratio where the cut length is the hypotenuse and the board width is the opposite side: $$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1.5}{2}$$\n\n3. **Calculate angle:** $$\theta = \sin^{-1}\left(\frac{1.5}{2}\right)$$\n\n4. **Evaluate:** $$\frac{1.5}{2} = 0.75$$\n$$\theta = \sin^{-1}(0.75) \approx 48.6^\circ \approx 49^\circ$$