An Obtuse Triangle is a triangle that has one angle greater than $90^\circ$ (an obtuse angle). Because the internal angles of any triangle add up to $180^\circ$, the other two angles must be acute (less than $90^\circ$).
Visually, it looks “reclined” or “leaning back.” Calculating its area can be tricky because the altitude (height) often falls *outside* the triangle’s base.
Calculator Features
1. Obtuse Verification
Not sure if your triangle is actually obtuse? Our tool checks the calculated angles. If the largest angle is $\le 90^\circ$, it warns you that you are working with an Acute or Right triangle instead.
2. Flexible Inputs
Whether you are measuring land or solving a textbook problem, use the mode that fits your data:
Base & Height: Works even if the height is external.
SSS & SAS: Perfect for physical measurements where you cannot easily find the height.
3. Dynamic Visuals
The interactive diagram updates to match your inputs, showing you exactly how “wide” the obtuse angle causes the shape to stretch.
Formulas
Method 1: Base & Height
The universal formula applies, but remember $h$ is the perpendicular distance, not the side length.
Area $A = \frac{1}{2} b h$
Method 2: SAS (Side-Angle-Side)
If you know the obtuse angle $\gamma$ and the two sides forming it ($a$ and $b$):
Area $A = \frac{1}{2} a b \sin(\gamma)$
Method 3: Heron’s Formula (SSS)
Input all three sides ($a, b, c$). Determine semi-perimeter $s$:
Area $A = \sqrt{s(s-a)(s-b)(s-c)}$
Real-World Applications
Architecture
Modern “A-frame” cabins or avant-garde buildings often use obtuse triangles in their facades or roof lines to create distinct, non-traditional silhouettes.
Aviation
Swept-back wings on aircraft often form obtuse angles relative to the fuselage. Calculating their surface area is vital for lift and drag analysis.
Land Surveying
Property lines often meet at obtuse angles (corners $> 90^\circ$). Surveyors treat these plot corners as vertices of obtuse triangles when calculating total acreage.
Tips & Tricks
Height Confusion
For an obtuse triangle, if you extend the base line, the height line drops down to meet it *outside* the triangle. Don’t try to measure height “inside” the shape unless you are splitting it.
Angle Sum check
If you are using ASA mode, insure $\alpha + \beta < 180^\circ$. For an obtuse triangle, the two acute angles will be quite small (their sum must be $< 90^\circ$).
Frequently Asked Questions (FAQs)
1. Can a triangle have two obtuse angles?
Impossible. Since the sum of angles is $180^\circ$, and one obtuse angle is $> 90^\circ$, the remaining $90^\circ$ (or less) must be shared by two acute angles.
2. How do I find the longest side?
The longest side is always opposite the largest angle. In an obtuse triangle, the side opposite the obtuse angle is always the longest.
3. Is perimeter just sum of sides?
Yes. Perimeter $P = a + b + c$. This never changes regardless of angles.
Final Words
The Obtuse Triangle Area Calculator handles the quirks of “reclined” geometry seamlessly. It confirms your shape is truly obtuse and delivers precise area, perimeter, and angle data in an instant.
